Shifting Functions Math Example 3

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Example 3

easy
The point (4,7)(4, 7) is on the graph of y=f(x)y=f(x). Find the corresponding point on each shifted graph: (a) y=f(x−1)+3y=f(x-1)+3, (b) y=f(x+5)−2y=f(x+5)-2.

Solution

  1. 1
    (a) Shift right 11, up 33: (4+1,7+3)=(5,10)(4+1, 7+3)=(5, 10).
  2. 2
    (b) Shift left 55, down 22: (4−5,7−2)=(−1,5)(4-5, 7-2)=(-1, 5).

Answer

(a) (5,10)(5,10); (b) (−1,5)(-1,5)
Each point (x,y)(x,y) on the original graph maps to (x+h,y+k)(x+h, y+k) on the shifted graph f(x−h)+kf(x-h)+k. Left/right shifts change xx; up/down shifts change yy.

About Shifting Functions

Shifting a function translates its graph horizontally or vertically without changing its shape: f(x−h)+kf(x - h) + k shifts right by hh and up by kk.

Learn more about Shifting Functions →

More Shifting Functions Examples

Example 1 easy

Starting from [formula], describe and sketch the transformations for [formula].

Example 2 medium

The graph of [formula] is shifted left [formula] units and down [formula] units to give [formula]. W

Example 4 medium

Write the equation of the function whose graph is [formula] shifted right [formula] and reflected ov

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Related Concepts

Function Transformation