Question

Use the function f(x)=|x+4|−2, and its transformation t(x)=|4x+4|−2, to answer the question.

Which statement correctly describes the transformation that maps f to t?

A The mapping statement is f(x)→f(4x), so the vertex will move left by four units, and the transformed function will be wider.

B The mapping statement is f(x)→4f(x) , so the vertex will move left by three units, and the transformed function will be wider.

C The mapping statement is f(x)→4f(x), so the vertex will move right by four units, and the transformed function will be narrower.

D The mapping statement is f(x)→f(4x), so the vertex will move right by three units, and the transformed function will be narrower.

Answer 1

first, eliminate A and B. the coefficient of x changes from 1 to 4, the graph rises 4 times faster, so the graph will be narrower, not wider.
x changes to 4x,nothing else changes.
the original vertex is when x+4=0, x=-4
the new vertex is when 4x+4=0, x=-1
from -4 to -1, it is a shift to the right by three units,
so the answer should be D.