Question

if f(x) = |x| and g(x) = |x| − 4, which transformation is applied to f(x) to get g(x)? a vertical transformation of f(x) four units upward a horizontal transformation of f(x) four units to the left a horizontal transformation of f(x) four units to the right a vertical transformation of f(x) four units downward

Answer 1

The correct option is D. A vertical transformation of f(x) four units downward

Explanation:

The function f(x) = |x| and the function g(x) = |x| - 4

A). A vertical transformation of f(x) four units upward :

f(x) = f(x) + 4

⇒ f(x) = |x| + 4 ≠ g(x)

B). A horizontal transformation of f(x) four units to the left

f(x) = f(x + 4)

⇒ f(x) = |x + 4| ≠ g(x)

C). A horizontal transformation of f(x) four units to the right

f(x) = f(x - 4)

⇒ f(x) = |x - 4| ≠ g(x)

D). A vertical transformation of f(x) four units downward

f(x) = f(x) - 4

⇒ f(x) = |x| - 4 = g(x)

Therefore, The correct option is D. A vertical transformation of f(x) four units downward

Answer 2

g(x) = |x| − 4 is obtained from f(x) = |x| by applying a vertical transformation of f(x) four units downwards.