Question

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.

Answer 1

The domain and the range of a function are the set of input and output values, the function can take.

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

Given

$g(x) = 9x^2 - 2$

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 $(-\infty, \infty)$

$(-\infty, \infty)$ is in interval notation

The corresponding set notation is: $- \infty < x < \infty$

The parent function

We have:

$f(x) = x^2$

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

The rule of this transformation is:

$(x,y) \to (x,9y)$

So, we have:

$f'(x) = 9x^2$

Next, the function is shifted down by 5 units.

So, we have:

$g(x) = f'(x) - 5$

$g(x) = 9x^2 - 5$

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