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Chapter 2: Q. 1 (page 112)

Suppose that the graph of a function f is known. Then the graph of y=f(x-2)may be obtained by a(n) ________ shift of the graph of f to the ________ a distance of2 units.

Short Answer

Expert verified

horizontal; right

Step by step solution

01

Step 1. Concept Used

If the argument xof a function fis replaced by x-h, h>0, the graph of the new function y=f(x-h)is the graph of fshifted horizontally right hunits.

If the argument xof a function fis replaced by x+h, h>0, the graph of the new function y=f(x+h)is the graph of f shifted horizontally left h units.

02

Step 2. Fill in the blanks

When the argument xof a function fis replaced by x-2, then the new function y=f(x-2)is the graph of fshifted horizontally right 2units.

So if the graph of a function fis known. Then the graph of y=f(x-2)may be obtained by a horizontal shift of the graph of fto the right a distance of2units.

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