Reflecting Functions Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
The point (−3,7)(-3, 7) is on the graph of y=f(x)y=f(x). Give the corresponding point on: (a) y=−f(x)y=-f(x), (b) y=f(−x)y=f(-x), (c) y=−f(−x)y=-f(-x).

Solution

  1. 1
    (a) y=−f(x)y=-f(x): negate yy-coordinate → (−3,−7)(-3, -7).
  2. 2
    (b) y=f(−x)y=f(-x): negate xx-coordinate → (3,7)(3, 7).
  3. 3
    (c) y=−f(−x)y=-f(-x): negate both coordinates → (3,−7)(3, -7).

Answer

(a) (−3,−7)(-3,-7); (b) (3,7)(3,7); (c) (3,−7)(3,-7)
Each reflection transforms the coordinates of every point: xx-axis reflection negates yy; yy-axis reflection negates xx; reflecting over both axes (or rotating 180°180° around origin) negates both coordinates.

About Reflecting Functions

Reflecting a function mirrors its graph across the xx-axis (−f(x)-f(x)), yy-axis (f(−x)f(-x)), or the line y=xy = x (the inverse function).

Learn more about Reflecting Functions →

More Reflecting Functions Examples

Example 1 easy

Given [formula], write the equations for (a) reflection over the [formula]-axis and (b) reflection o

Example 2 medium

Show that [formula] is unchanged by reflection over the [formula]-axis (even function) but [formula]

Example 4 hard

Classify [formula] and [formula] as even, odd, or neither. Explain using the definitions.

← All Reflecting Functions Examples Reflecting Functions Concept