Question

How does the graph of f(x) = -2^3x -4 differ from the graph of g(x) = -2^3x?

A. The graph of f(x) is shifted four units down from the graph of g(x).
B. The graph of f(x) is shifted four units to the left of the graph of g(x).
C. The graph of f(x) is shifted four units to the right of the graph of g(x).
D. The graph of f(x) is shifted four units up from the graph of g(x).

Answer 1

The answer is letter a

Answer 2

Option: A is the correct answer.

A. The graph of f(x) is shifted four units down from the graph of g(x).

Explanation:

We know that for any parent function g(x) the transformed function g(x)+k is a shift of the function g(x) k units up or down depending on the value of k

i.e. if k>0 then the shift is k units up

and if k<0 then the shift is k units down.

Hence, here we have parent function g(x) as:

`g(x)=-2^(3x)`

and we are given transformed function f(x) as:

`f(x)=-2^(3x)-4`

This means we have k=-4<0

This means that the function f(x) is the shift of the parent function g(x) 4 units down.