Graph reflection is an important concept in algebra, coordinate geometry, and mathematical transformations. It helps us understand how a function changes when its graph is reflected across an axis, the origin, or a diagonal line.
Reflection Graph Calculator
Whether you are studying functions, solving algebra problems, or analyzing coordinate transformations, understanding graph reflections is essential for interpreting mathematical relationships.
Our Reflection Graph Calculator is a free online tool designed to calculate and visualize reflections of mathematical functions across different axes and lines.
The calculator supports four types of functions: linear, quadratic, absolute value, and cubic functions.
You can reflect these functions across the X-axis, Y-axis, origin, line y = x, or line y = −x.
Instead of manually plotting coordinates and applying reflection formulas, you can enter the function coefficients, select the reflection type, and generate the original and reflected graphs.
The tool displays the original function, reflection rule, transformed coordinate values, and a graphical comparison between the original and reflected curves.
It also provides a coordinate table showing how selected points change after reflection.
This makes the calculator useful for students, teachers, mathematics enthusiasts, and anyone learning about graph transformations.
In this guide, we will explain how to use the Reflection Graph Calculator, understand different reflection formulas, solve practical examples, and explore important properties of reflected functions.
What Is a Reflection Graph Calculator?
A Reflection Graph Calculator is an online mathematical tool that helps visualize how the graph of a function changes when reflected across a specified axis or line.
In mathematics, reflection is a geometric transformation that produces a mirror image of an original object.
When applied to a function, reflection changes the coordinates of points on its graph according to a specific transformation rule.
For example, consider the linear function:
y = x + 2
If this function is reflected across the X-axis, every Y-coordinate changes sign.
The reflected function becomes:
y = −x − 2
Similarly, reflecting the same function across the Y-axis changes the sign of the X-variable.
The reflected function becomes:
y = −x + 2
These transformations produce different graphs.
Our calculator helps visualize these differences by displaying both the original and reflected curves on the same coordinate plane.
It also shows the coordinate transformation rule used for the selected reflection.
What Is Graph Reflection?
Graph reflection is a transformation that flips a graph across a fixed line.
The fixed line is called the line of reflection.
Every point on the original graph is mapped to a corresponding point on the opposite side of the reflection line.
For line reflections, the original point and its reflected image are equally distant from the reflection line.
Suppose the original point is:
P(x, y)
After reflection, the new point is:
P′(x′, y′)
The reflected coordinates depend on the selected reflection rule.
For example:
Reflection across X-axis:
(x, y) → (x, −y)
Reflection across Y-axis:
(x, y) → (−x, y)
Reflection across y = x:
(x, y) → (y, x)
These rules can be applied to individual points or entire graphs.
When every point on a function is reflected, the result is a new graph representing the transformed relationship.
How to Use the Reflection Graph Calculator
Our online Reflection Graph Calculator allows you to visualize reflections of different mathematical functions.
Follow these steps to calculate and graph a reflection.
Step 1: Select the Function Type
Choose the mathematical function you want to reflect.
Available options include:
- Linear: y = mx + b
- Quadratic: y = ax² + bx + c
- Absolute Value: y = a|x − h| + k
- Cubic: y = ax³ + bx + c
Each function requires different coefficients.
Step 2: Enter the Function Coefficients
Enter the coefficient values corresponding to your selected function.
For a linear function:
y = mx + b
Enter the slope m and intercept b.
For a quadratic function:
y = ax² + bx + c
Enter coefficients a, b, and c.
For an absolute value function:
y = a|x − h| + k
Enter a, h, and k.
For a cubic function:
y = ax³ + bx + c
Enter a, b, and c.
Step 3: Select the Reflection Axis
Choose where you want to reflect the function.
Available options include:
No Reflection
X-axis
Y-axis
Origin
Line y = x
Line y = −x
Selecting No Reflection displays the original function without changing its coordinates.
Step 4: Enter the X-Axis Range
Enter the minimum and maximum X-values for the graph.
For example:
Minimum X = −10
Maximum X = 10
The calculator uses these values to determine the portion of the original function being graphed.
The maximum X-value must be greater than the minimum X-value.
The calculator supports an X-range width of up to 200 units.
Step 5: Click Calculate
After entering the required values, click the Calculate button.
The calculator generates the original and reflected graphs.
Step 6: Review the Results
The result section displays the original function, reflection description, transformation rule, intercept information, graph, and coordinate table.
The graph uses two colors:
Blue: Original function
Orange: Reflected function
This makes it easier to compare the two graphs.
Step 7: Examine the Coordinate Table
The coordinate table displays selected points from the original and reflected graphs.
Each row includes:
Original X-coordinate
Original Y-coordinate
Reflected X-coordinate
Reflected Y-coordinate
These values help explain how the reflection transformation changes individual points.
Step 8: Reset the Calculator
Click Reset to clear the current settings and return to the default calculator values.
You can then calculate another graph reflection.
Graph Reflection Formulas
Different reflection types require different mathematical formulas.
Understanding these formulas helps explain how a graph changes after reflection.
1. Reflection Across the X-Axis
Reflecting a function across the X-axis changes the sign of every Y-coordinate.
Coordinate Rule:
(x, y) → (x, −y)
Function Formula:
g(x) = −f(x)
Where:
f(x) = Original function
g(x) = Reflected function
Example: Reflect y = 2x + 3 Across the X-Axis
Original function:
f(x) = 2x + 3
Apply the reflection formula:
g(x) = −f(x)
Substitute the function:
g(x) = −(2x + 3)
Distribute the negative sign:
g(x) = −2x − 3
Answer: The reflected function is y = −2x − 3.
Every point on the original graph moves to the opposite side of the X-axis.
For example:
Original point: (1, 5)
Reflected point: (1, −5)
The X-coordinate remains unchanged.
Only the Y-coordinate changes sign.
2. Reflection Across the Y-Axis
Reflection across the Y-axis changes the sign of every X-coordinate.
Coordinate Rule:
(x, y) → (−x, y)
Function Formula:
g(x) = f(−x)
This means replacing every occurrence of x with −x.
Example: Reflect y = x² + 3x + 2 Across the Y-Axis
Original function:
f(x) = x² + 3x + 2
Apply the formula:
g(x) = f(−x)
Substitute −x into the function:
g(x) = (−x)² + 3(−x) + 2
Simplify:
g(x) = x² − 3x + 2
Answer: The reflected function is y = x² − 3x + 2.
Notice that the squared term remains positive because:
(−x)² = x²
However, the linear term changes sign.
This produces a horizontal mirror image across the Y-axis.
3. Reflection Across the Origin
Reflection across the origin changes the signs of both coordinates.
Coordinate Rule:
(x, y) → (−x, −y)
Function Formula:
g(x) = −f(−x)
This transformation is equivalent to rotating the graph 180 degrees around the origin.
Example: Reflect y = x² + 2x + 1 Across the Origin
Original function:
f(x) = x² + 2x + 1
Apply the formula:
g(x) = −f(−x)
First, replace x with −x.
f(−x) = (−x)² + 2(−x) + 1
Simplify:
f(−x) = x² − 2x + 1
Now multiply by −1.
g(x) = −(x² − 2x + 1)
g(x) = −x² + 2x − 1
Answer: The reflected function is y = −x² + 2x − 1.
The graph is rotated 180 degrees around the origin.
4. Reflection Across the Line y = x
Reflecting a graph across the line y = x swaps the X and Y coordinates.
Coordinate Rule:
(x, y) → (y, x)
For an original function:
y = f(x)
The reflected relation becomes:
x = f(y)
This transformation is closely related to inverse functions.
However, the reflected graph is not always a function of x.
Example: Reflect y = 2x + 4 Across y = x
Original function:
y = 2x + 4
Swap x and y:
x = 2y + 4
Solve for y:
x − 4 = 2y
y = (x − 4) / 2
Simplify:
y = 0.5x − 2
Therefore, the reflected graph is:
y = 0.5x − 2
This is the inverse function of the original linear function.
Important Note
Not every function has an inverse that is also a function over its full domain.
For example, reflecting:
y = x²
Across y = x produces:
x = y²
Solving for y gives:
y = ±√x
The reflected graph has two branches.
It fails the vertical line test for positive x-values.
Therefore, the reflection is a relation rather than a single-valued function.
Our calculator plots transformed coordinates, allowing it to display these reflections even when the result is not a conventional function.
5. Reflection Across the Line y = −x
Reflection across y = −x swaps the coordinates and changes both signs.
Coordinate Rule:
(x, y) → (−y, −x)
For an original function:
y = f(x)
The reflected relation can be written as:
x = −f(−y)
Example: Reflect y = 2x + 3 Across y = −x
Original function:
y = 2x + 3
Apply the coordinate transformation.
Swap and negate the coordinates:
x = −f(−y)
Substitute the original function:
x = −[2(−y) + 3]
Simplify:
x = 2y − 3
Solve for y:
2y = x + 3
y = 0.5x + 1.5
Therefore, the reflected function is:
y = 0.5x + 1.5
This transformation produces a mirror image across the line y = −x.
6. No Reflection
The calculator also provides a No Reflection option.
When this option is selected, the original coordinates remain unchanged.
Coordinate Rule:
(x, y) → (x, y)
The resulting function is:
g(x) = f(x)
This option is useful when you want to visualize the original graph before applying a transformation.
Reflection Rules Summary
The following formulas describe the reflection methods supported by the calculator.
| Reflection Type | Coordinate Rule | Function Transformation |
|---|---|---|
| X-Axis | (x, y) → (x, −y) | g(x) = −f(x) |
| Y-Axis | (x, y) → (−x, y) | g(x) = f(−x) |
| Origin | (x, y) → (−x, −y) | g(x) = −f(−x) |
| Line y = x | (x, y) → (y, x) | x = f(y) |
| Line y = −x | (x, y) → (−y, −x) | x = −f(−y) |
| No Reflection | (x, y) → (x, y) | g(x) = f(x) |
These formulas are useful for both algebraic calculations and graphical transformations.
How to Reflect a Linear Function
A linear function has the general form:
y = mx + b
Where:
m = Slope
b = Y-intercept
Linear functions produce straight-line graphs.
Example: Reflect y = 3x − 2 Across the X-Axis
Original function:
f(x) = 3x − 2
Apply:
g(x) = −f(x)
Therefore:
g(x) = −(3x − 2)
g(x) = −3x + 2
The original slope is 3.
The reflected slope is −3.
The original Y-intercept is −2.
The reflected Y-intercept is 2.
This transformation reverses the vertical direction of the graph.
Reflecting the Same Function Across the Y-Axis
Original:
f(x) = 3x − 2
Apply:
g(x) = f(−x)
g(x) = 3(−x) − 2
g(x) = −3x − 2
In this case, the slope changes sign while the Y-intercept remains unchanged.
How to Reflect a Quadratic Function
A quadratic function has the general form:
y = ax² + bx + c
Quadratic functions produce parabolic graphs.
The coefficient a determines whether the parabola opens upward or downward.
Example: Reflect y = x² − 4x + 3 Across the X-Axis
Original function:
f(x) = x² − 4x + 3
Apply:
g(x) = −f(x)
Substitute:
g(x) = −(x² − 4x + 3)
Simplify:
g(x) = −x² + 4x − 3
The original parabola opens upward.
The reflected parabola opens downward.
This happens because the leading coefficient changes from positive to negative.
Reflecting the Same Quadratic Across the Y-Axis
Original:
f(x) = x² − 4x + 3
Apply:
g(x) = f(−x)
g(x) = (−x)² − 4(−x) + 3
Simplify:
g(x) = x² + 4x + 3
The reflected parabola remains upward-opening.
However, its horizontal position changes.
How to Reflect an Absolute Value Function
An absolute value function has the general form:
y = a|x − h| + k
Where:
a = Vertical stretch or reflection coefficient
h = Horizontal shift
k = Vertical shift
The graph typically has a V-shape.
Its vertex is located at:
(h, k)
Example: Reflect y = |x − 2| + 3 Across the X-Axis
Original function:
f(x) = |x − 2| + 3
Apply the reflection formula:
g(x) = −f(x)
Substitute:
g(x) = −(|x − 2| + 3)
Simplify:
g(x) = −|x − 2| − 3
The original graph opens upward.
The reflected graph opens downward.
The original vertex is:
(2, 3)
The reflected vertex is:
(2, −3)
Reflection Across the Y-Axis
Original function:
f(x) = |x − 2| + 3
Apply:
g(x) = f(−x)
g(x) = |−x − 2| + 3
Using the absolute value property:
|−x − 2| = |x + 2|
Therefore:
g(x) = |x + 2| + 3
The reflected vertex becomes:
(−2, 3)
This shows how Y-axis reflection changes the horizontal position of the vertex.
How to Reflect a Cubic Function
The calculator supports cubic functions in the form:
y = ax³ + bx + c
This is a cubic expression without an x² term.
Cubic functions can produce S-shaped curves and may have different turning-point behavior depending on their coefficients.
Example: Reflect y = x³ + 2x − 1 Across the X-Axis
Original function:
f(x) = x³ + 2x − 1
Apply:
g(x) = −f(x)
Substitute:
g(x) = −(x³ + 2x − 1)
Simplify:
g(x) = −x³ − 2x + 1
The reflected graph is the vertical mirror image of the original graph.
Reflection Across the Y-Axis
Apply:
g(x) = f(−x)
g(x) = (−x)³ + 2(−x) − 1
Simplify:
g(x) = −x³ − 2x − 1
The cubic and linear terms change signs.
The constant term remains unchanged.
How Reflection Changes the Y-Intercept
The Y-intercept is the point where a graph crosses the Y-axis.
It occurs when:
x = 0
For a function:
y = f(x)
The Y-intercept is:
(0, f(0))
Different reflections affect the Y-intercept differently.
X-Axis Reflection
The Y-intercept changes sign.
For example:
Original Y-intercept = (0, 4)
Reflected Y-intercept = (0, −4)
Y-Axis Reflection
The Y-intercept remains unchanged.
For example:
Original Y-intercept = (0, 4)
Reflected Y-intercept = (0, 4)
Origin Reflection
The Y-intercept changes sign.
For example:
Original Y-intercept = (0, 4)
Reflected Y-intercept = (0, −4)
Diagonal Reflections
Reflections across y = x or y = −x exchange coordinate roles.
The reflected Y-intercepts depend on the original function's X-intercepts.
For example, if the original graph contains:
(3, 0)
Reflecting across y = x produces:
(0, 3)
Therefore, the reflected graph has a Y-intercept at (0, 3).
A reflected relation may have multiple Y-intercepts or none, depending on the original function.
Calculator note: The tool directly displays the reflected Y-intercept for X-axis reflection and no reflection. For other reflection types, it directs users to the graph and coordinate table rather than calculating an explicit intercept.
Understanding the Reflection Graph
Our Reflection Graph Calculator displays two curves on the same coordinate plane.
The original function appears in blue.
The reflected function appears in orange.
This allows you to compare the shapes and positions of both graphs.
For example, reflecting a parabola across the X-axis produces a vertically inverted parabola.
Reflecting a graph across the Y-axis produces a horizontal mirror image.
Reflecting across the origin produces a 180-degree rotation around the origin.
When reflecting across y = x or y = −x, the coordinate directions are exchanged.
The calculator automatically adjusts the graph scale to include the calculated original and reflected coordinates.
The selected X-range controls the portion of the original function used for graphing.
After reflection, the transformed X-values may extend beyond the original range.
This is especially common for diagonal reflections.
Understanding the Coordinate Table
The coordinate table helps explain how individual points move during reflection.
Consider the function:
y = x + 2
Suppose we select reflection across the X-axis.
The transformation rule is:
(x, y) → (x, −y)
Some corresponding points are:
| Original X | Original Y | Reflected X | Reflected Y |
|---|---|---|---|
| −2 | 0 | −2 | 0 |
| −1 | 1 | −1 | −1 |
| 0 | 2 | 0 | −2 |
| 1 | 3 | 1 | −3 |
| 2 | 4 | 2 | −4 |
Notice that the reflected X-coordinates remain unchanged.
However, the Y-coordinates change signs.
The coordinate table provides a numerical explanation of the graph transformation.
Our calculator automatically generates selected coordinate pairs based on the function and X-range you enter.
Reflection vs. Translation vs. Rotation
Reflection is one of several important graph transformations.
Understanding the differences helps prevent confusion.
Reflection
Reflection flips a graph across a fixed line.
Example:
f(x) = x²
Reflection across X-axis:
g(x) = −x²
Translation
Translation moves a graph horizontally or vertically without changing its orientation.
Example:
f(x) = x²
Shift upward by 3 units:
g(x) = x² + 3
Rotation
Rotation turns a graph around a fixed point by a specified angle.
For example, rotating a point 180 degrees around the origin transforms:
(x, y) → (−x, −y)
This produces the same coordinate transformation as reflection through the origin.
However, a 180-degree rotation is not the same geometric operation as reflection across a single line.
Properties of Graph Reflection
Graph reflections have several important mathematical properties.
1. Distance Preservation
Reflection preserves distances between points.
If two points are 5 units apart before reflection, their reflected images will also be 5 units apart.
2. Shape Preservation
Reflection does not distort the shape of a graph.
Straight lines remain straight lines.
Parabolas remain parabolas as geometric curves, although their orientations may change.
3. Mirror Symmetry
A graph and its reflection are symmetric about the selected reflection line.
4. Reversibility
Applying the same reflection twice returns the original graph.
For example:
f(x) = x² + 2
First reflection across X-axis:
g(x) = −x² − 2
Second reflection across X-axis:
h(x) = x² + 2
The original function is restored.
5. Domain and Range Changes
Some reflections affect the domain and range of a function.
For X-axis reflection, the domain remains unchanged while the range changes sign.
For Y-axis reflection, the domain is reflected horizontally while the range remains unchanged.
For reflection across y = x, the original domain and range exchange roles in the reflected relation.
These properties are useful when analyzing transformed functions.
Applications of the Reflection Graph Calculator
Graph reflection is useful in many educational and practical situations.
1. Algebra Education
Students use graph reflections to understand function transformations and coordinate relationships.
2. Coordinate Geometry
Reflection rules help solve problems involving points, lines, curves, and symmetry.
3. Precalculus
Graph transformations are important when studying polynomial functions, absolute value functions, and inverse relationships.
4. Calculus
Reflection properties help students understand function behavior, symmetry, and graphical relationships.
5. Computer Graphics
Coordinate reflections are used to create mirrored objects and geometric transformations.
6. Engineering Mathematics
Engineers use coordinate transformations when analyzing mathematical models and geometric relationships.
7. Physics
Symmetry and coordinate transformations are important in many areas of physics.
8. Teaching and Learning
Teachers can use reflected graphs to demonstrate how mathematical equations change under different transformations.
Benefits of Using Our Online Reflection Graph Calculator
Our calculator provides several useful features.
Multiple Function Types: Supports linear, quadratic, absolute value, and cubic functions.
Different Reflection Methods: Reflect graphs across the X-axis, Y-axis, origin, y = x, and y = −x.
Visual Graph Comparison: View original and reflected curves together.
Coordinate Table: Examine how individual points transform.
Reflection Rules: Understand the coordinate transformation used.
Custom X-Range: Select the portion of the original function you want to graph.
Original Function Display: Review the equation used to generate the graph.
Y-Intercept Information: View available intercept information for the selected transformation.
Free Online Access: Perform calculations without registration or payment.
These features make the calculator helpful for learning and practicing graph reflections.
Common Mistakes When Reflecting Functions
Graph reflection problems can produce incorrect answers when transformation rules are applied improperly.
Confusing X-Axis and Y-Axis Reflection
For X-axis reflection:
g(x) = −f(x)
For Y-axis reflection:
g(x) = f(−x)
These operations are different.
Forgetting Parentheses
When reflecting across the X-axis, the negative sign applies to the entire function.
For example:
f(x) = x² + 3x + 2
Correct:
g(x) = −(x² + 3x + 2)
g(x) = −x² − 3x − 2
Incorrectly Simplifying Even Powers
Remember:
(−x)² = x²
Therefore, an x² term does not change sign under Y-axis reflection.
Confusing y = x Reflection with Y-Axis Reflection
Reflection across y = x swaps the X and Y coordinates.
It does not simply change the sign of x.
Assuming Every Reflected Relation Is a Function
A reflection across y = x may produce a relation that fails the vertical line test.
For example, reflecting y = x² produces x = y².
This relation has two branches.
Using an Incorrect Graph Range
A very narrow X-range may not show enough of the original function to understand its shape.
Choose a range appropriate for the function being studied.
Tips for Accurate Graph Reflection Calculations
To calculate graph reflections accurately, start by identifying the original function.
Next, determine the line or axis of reflection.
Write the appropriate transformation formula before simplifying the equation.
For X-axis reflection, negate the entire function.
For Y-axis reflection, replace x with −x.
For origin reflection, use −f(−x).
For diagonal reflections, transform coordinates directly and remember that the reflected graph may not be a single-valued function.
When interpreting the graph, compare corresponding points rather than relying only on the visual appearance.
Use the coordinate table to verify how the reflection affects X and Y values.
Finally, choose an appropriate X-range so that the graph shows the important features of the original function.
Frequently Asked Questions (FAQs)
1. What is a Reflection Graph Calculator?
A Reflection Graph Calculator is an online mathematical tool that calculates and displays the reflection of a function across an axis or line.
It helps visualize graph transformations and corresponding coordinate changes.
2. How do you reflect a graph across the X-axis?
To reflect a graph across the X-axis, multiply the function by −1.
Formula:
g(x) = −f(x)
For example:
f(x) = x² + 2
Reflected function:
g(x) = −x² − 2
3. How do you reflect a graph across the Y-axis?
Replace x with −x in the original function.
Formula:
g(x) = f(−x)
For example:
f(x) = x² + 3x
Reflected function:
g(x) = x² − 3x
4. What is the formula for reflection across the origin?
The formula is:
g(x) = −f(−x)
This transformation changes the signs of both coordinates and is equivalent to a 180-degree rotation around the origin.
5. How do you reflect a graph across y = x?
Swap the X and Y coordinates.
Coordinate rule:
(x, y) → (y, x)
For a function y = f(x), the reflected relation becomes x = f(y).
6. How do you reflect a graph across y = −x?
Swap the coordinates and change both signs.
Coordinate rule:
(x, y) → (−y, −x)
The reflected relation satisfies:
x = −f(−y)
7. Can this calculator reflect quadratic functions?
Yes. The calculator supports quadratic functions in the form:
y = ax² + bx + c
You can enter coefficients a, b, and c and select the desired reflection method.
8. Can I reflect an absolute value function?
Yes. The calculator supports absolute value functions in the form:
y = a|x − h| + k
You can enter the coefficient and shift values to graph the original and reflected functions.
9. Does the calculator support cubic functions?
Yes. It supports cubic functions in the form:
y = ax³ + bx + c
This is a cubic expression without an x² term.
You can reflect it across the supported axes and lines.
10. What happens when a parabola is reflected across the X-axis?
A parabola opening upward becomes a parabola opening downward.
For example:
Original:
y = x²
Reflected:
y = −x²
The vertex remains on the X-axis if its original Y-coordinate is zero.
11. Does reflection change the shape of a graph?
No. Reflection preserves distances and geometric shape.
However, it changes the orientation or position of the graph relative to the reflection line.
12. What happens when a graph is reflected twice?
Reflecting a graph twice across the same line returns it to its original position.
This is because reflection is a reversible transformation.
13. Can the reflected graph have a different domain and range?
Yes. Reflections can change the domain and range.
For example, reflection across the X-axis changes the signs of range values.
Reflection across y = x exchanges the domain and range of the original relation.
14. Why does the calculator show a coordinate table?
The coordinate table displays selected original and reflected points.
It helps explain how the transformation changes individual coordinates and allows users to verify reflection rules.
15. Is the Reflection Graph Calculator free to use?
Yes. Our online Reflection Graph Calculator is completely free.
You can graph and reflect supported mathematical functions, examine coordinate transformations, and compare original and reflected curves without registration.
Conclusion
Graph reflection is a fundamental mathematical transformation used in algebra, coordinate geometry, precalculus, and many other areas of mathematics.
Understanding how functions reflect across the X-axis, Y-axis, origin, and diagonal lines helps explain the relationship between equations and their graphical representations.
The most important reflection formulas include:
X-Axis Reflection: g(x) = −f(x)
Y-Axis Reflection: g(x) = f(−x)
Origin Reflection: g(x) = −f(−x)
Reflection Across y = x: (x, y) → (y, x)
Reflection Across y = −x: (x, y) → (−y, −x)
Our free online Reflection Graph Calculator simplifies these transformations by allowing you to enter function coefficients, choose a reflection method, and view original and reflected graphs together.
It supports linear, quadratic, absolute value, and cubic functions, making it useful for a variety of algebra and geometry problems.
The coordinate table also helps explain how individual points move during reflection, providing a connection between algebraic formulas and graphical transformations.
Whether you are studying mathematical functions, practicing coordinate geometry, or teaching graph transformations, this calculator provides a convenient way to explore reflection concepts.
Use the Reflection Graph Calculator above to reflect linear, quadratic, cubic, and absolute value functions across supported axes and lines, and visualize the results with an interactive coordinate graph and transformation table.