Advanced Reflection Function Calculator

Enter Function and Reflection Settings

Function type

Reflection type

h reference value

Used for x = h or point reflections.

a coefficient

b coefficient

c coefficient / shift

d coefficient / shift

k reference value

Used for y = k or point reflections.

x minimum

x maximum

Step size

This calculator builds mapped points for the reflected graph. For vertical-line and point reflections, it shows coordinate mapping directly and also provides the transformed rule.

Original x	Original y	Reflected x	Reflected y
-2	-3	2	-3
-1	-1	1	-1
0	1	0	1
1	3	-1	3
2	5	-2	5

Formula Used

Reflections change graph positions by remapping coordinates or by replacing inputs and outputs inside the function rule.

Across x-axis: g(x) = -f(x)
Across y-axis: g(x) = f(-x)
Across origin: g(x) = -f(-x)
Across vertical line x = h: g(x) = f(2h - x)
Across horizontal line y = k: g(x) = 2k - f(x)
About point (h, k): g(x) = 2k - f(2h - x)

The calculator first evaluates the original function over the chosen x-range. It then applies the selected reflection rule to each point, producing mapped coordinates for the reflected graph.

How to Use This Calculator

Select a function family such as quadratic, absolute value, sine, or logarithmic.
Enter the needed coefficients or shifts shown by the parameter labels.
Choose the reflection type: axis, custom line, origin, or point.
Enter h or k if your reflection uses a custom line or point.
Set the x minimum, x maximum, and step size for generated points.
Press Calculate Reflection to view the transformed rule and mapped coordinates.
Use the CSV or PDF buttons to export the result table.

Frequently Asked Questions

1. What does reflecting a function mean?

It means flipping every point of a graph across a chosen line or point. The shape stays related, but coordinates move according to a fixed reflection rule.

2. Why is the y-axis reflection written as f(-x)?

Reflecting across the y-axis changes each x-coordinate to its opposite. Replacing x with -x in the rule reproduces that same horizontal flip.

3. Why might some rows be missing?

Some functions are not defined for every x-value. Square roots need nonnegative radicands, logarithms need positive inputs, and reciprocals cannot divide by zero.

4. Does this calculator support trigonometric functions?

Yes. It includes sine and cosine models with adjustable amplitude, frequency, and shifts, so you can study reflections of periodic curves too.

5. What is the difference between reflecting across x = h and y = k?

Reflecting across x = h changes horizontal placement. Reflecting across y = k changes vertical placement. One flips x-values, while the other flips y-values.

6. What does reflecting about a point do?

Point reflection reverses both horizontal and vertical position around the chosen center. It is equivalent to a half-turn, also called 180-degree rotational symmetry.

7. Can I use decimals for coefficients and step size?

Yes. Decimal inputs are accepted for coefficients, shifts, line references, and x-steps, which helps with precise classroom, homework, or checking tasks.

8. What should I do if I get no valid points?

Try a different x-range, larger step, or corrected parameters. Also check whether the chosen model has restrictions, such as invalid logarithm bases or excluded domain values.

Reflection Function Calculator