Question

The functions f(x) and g(x) are described below:

f(x) = 32x + 8
g(x) = 32x − 9

The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units.

Answer 1

The graph of g(x) is obtained by shifting down the graph of f(x) by 17 units.

Explanation:

Given : The functions f(x) and g(x) are described below:

f(x) = 32x + 8 and g(x) = 32x − 9

To find : The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units.

Solution : We have given that

Parent function f(x) = 32x + 8

Transformed function g(x) = 32x − 9.

We can write it in form of parent by adding and subtracting 8 on right side

g(x) = 32x − 9 + 8 -8

g(x) = 32x + 8 -9 -8.

g(x) = 32x + 8 -17.

By the transformation rule we can write f(x) - k mean function f(x) is shifted down by k unit.

We can see The graph of g(x) is obtained by shifting down the graph of f(x) by 17 units.

Therefore, The graph of g(x) is obtained by shifting down the graph of f(x) by 17 units.

Answer 2

Suppose that the function f(x) is the parrent function and the graph of the function g(x)=f(x)-a can be obtained from the graph of the parrent function f(x) by shifting down a units.

Rewrite the expression for the function
`g(x)` in the following way:

`g(x)=32x-9=32x+8-8-9=32x+8-17=f(x)-17.`

This shows that the shift down is made by 17 units.

Answer: 17 units