Enter the domain and range of the function g(x) = 9x2 − 5 as an inequality, using set notation and using interval notation. Complete the explanation to compare the function to f(x) = x2 and describe the transformations.

The domain and the range of [tex]g(x) = 9x^2 - 2[/tex] is [tex](-\infty, \infty)[/tex].
The parent function [tex]f(x) =x^2[/tex] is vertically compressed by 9, then shifted down by 5 units to get [tex]g(x) = 9x^2 - 2[/tex]

Given

[tex]g(x) = 9x^2 - 2[/tex]

Domain and range

There is no restriction as to the input and the output of function g(x).

This means that the domain and the range are [tex](-\infty, \infty)[/tex]

[tex](-\infty, \infty)[/tex] is in interval notation

The corresponding set notation is: [tex]- \infty < x < \infty[/tex]

The parent function

We have:

[tex]f(x) = x^2[/tex]

First, the parent function is vertically compressed by a factor of 9.

The rule of this transformation is:

[tex](x,y) \to (x,9y)[/tex]

So, we have:

[tex]f'(x) = 9x^2[/tex]

Next, the function is shifted down by 5 units.

So, we have:

[tex]g(x) = f'(x) - 5[/tex]

[tex]g(x) = 9x^2 - 5[/tex]