Question

Each statement describes a transformation of the graph of f(x) = 3x. Which statement correctly describes the graph of g(x) = 3(x - 5) + 4?

A.
The graph of g(x) is the graph of f(x) translated up 4 units and left 5 units.

B.
The graph of g(x) is the graph of f(x) translated down 5 units and left 4 units.

C.
The graph of g(x) is the graph of f(x) translated down 5 units and right 4 units.

D.
The graph of g(x) is the graph of f(x) translated up 4 units and right 5 units.

Answer 1

D

Explanation:

We start with f(x) = 3x.

The graph of this function is a straight line thru the origin with slope 3.

The graph of g(x) = 3(x - 5) is the translation of the previous graph of 5 units to the right.

The graph of h(x) = 3(x - 5) + 4 is the translation of the previous graph 4 units up.

This matches Answer D.

Answer 2

D

Explanation:

Given f(x) then f(x ± a ) represents a horizontal translation parallel to the x- axis.

If + a then a shift of a units to the left ←

If - a then a shift of a units to the right →

Hence (x - 5) represents a shift of 5 units to the right →

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Given f(x) then f(x) ± c represents a vertical translation parallel to the y- axis.

If + c then a shift of c units vertically up ↑

If - c then a shift of c units vertically down ↓

Hence f(x) + 4 represents a shift of 4 units up ↑

Thus D is the correct statement