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.

Question

Mathematics

Ari Watson

28 March, 07:47

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.

+1

Answers (1)

Know the Answer?

Marc Henderson · 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.