Question

Select the correct answer. If and , which description represents the graph of function g? A. a horizontal transformation of function f 4 units right B. a vertical transformation of function f 4 units up C. a horizontal transformation of function f 4 units left D. a vertical transformation of function f 4 units down

Answer 1

The function g(x) = f(x-4) + 4 represents a horizontal transformation of function f by 4 units to the right and a vertical transformation of function f by 4 units up.

To see why, consider the effect of the two transformations on the graph of f.

A horizontal transformation of 4 units to the right means that every point on the graph of f(x) is shifted 4 units to the right.

A vertical transformation of 4 units up means that every point on the graph of f(x) is shifted 4 units up.

Therefore, the correct answer is A. a horizontal transformation of function f 4 units right.

Answer 2

A horizontal transformation of function f 4 units left ( the other guy is wrong... )

Hope this helps!

Explanation:

Ex: f(x) =
`(x - 2)^(2)` ; This is a horizontal transformation 2 units to the right and f(x) =
`(x+2)^(2)` ; is a horizontal transformation 2 units to the left.

Up and down : f(x) = (
`x^(2)` ) + 2 is up while f(x) = (
`x^(2)` ) - 2 is down.