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:

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

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

Read more about functions at:

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4 0

3 years ago

The following examples illustrate the associative property of multiplication.

kati45 [8]

Answer:

A) a • (b • c) = (a • b) • c

Step-by-step explanation:

The associative property of multiplication (or addition) shows that the order the numbers are multiplied it irrelevant, more specifically in the manners of parentheses.

So, the answer is A, which can also be seen in that substituting a as 5, b as 3, and c as 6 gives us the first example.

4 0

3 years ago

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