Practice Reflecting Functions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Reflecting a function mirrors its graph across the x-axis (-f(x)), y-axis (f(-x)), or the line y = x (the inverse function).
-f(x) flips over x-axis (upside down). f(-x) flips over y-axis (mirror).
Example 1
easyGiven f(x)=x^3-2, write the equations for (a) reflection over the x-axis and (b) reflection over the y-axis. Evaluate each at x=2.
Example 2
mediumShow that f(x)=x^2 is unchanged by reflection over the y-axis (even function) but f(x)=x^3 is negated by this reflection (odd function).
Example 3
easyThe point (-3, 7) is on the graph of y=f(x). Give the corresponding point on: (a) y=-f(x), (b) y=f(-x), (c) y=-f(-x).
Example 4
hardClassify f(x) = x^3 + x and g(x) = x^4 + x^2 + 1 as even, odd, or neither. Explain using the definitions.