Question

Write a function G that represents a vertical stretch by a factor of four and a horizontal shift five units right of the graph of f(x)=∣x∣?

A.G(x)=4∣x−5∣
B.G(x)=∣4x−5∣
C.G(x)=4∣x+5∣
D.G(x)=∣x+5∣

Answer 1

The correct function G that represents a vertical stretch by a factor of four and a horizontal shift five units right of the graph of f(x)=|x| is G(x) = 4|x-5|.

Step-by-step explanation:

The student is asked to write a function G that represents a vertical stretch by a factor of four and a horizontal shift five units to the right of the graph of f(x) = |x|. To stretch a function vertically by a factor, you multiply the function by that factor. Hence, the vertical stretch by four is achieved by multiplying |x| by 4, resulting in 4|x|. A horizontal shift to the right is accomplished by subtracting the shift amount from the variable x inside the absolute value. Therefore, a shift of five units to the right translates to (x - 5). Combining both transformations, the function G is 4|x-5|, which is option A: G(x) = 4|x-5|.