QuestionFind the function $g(x)$ that reflects $f(x)=|6x|-2$ in the $y$ -axis.

Studdy Solution

STEP 1

Assumptions1. The function $f(x) = |6x| -$ is given. We need to reflect this function in the $y$ -axis

STEP 2

A reflection in the $y$ -axis of a function $f(x)$ is achieved by replacing $x$ with $-x$ in the function. This is because when we reflect a point $(x, y)$ in the $y$ -axis, it becomes $(-x, y)$ .
So, to reflect the function $f(x)$ in the $y$ -axis, we replace $x$ with $-x$ in the function $f(x)$ .

STEP 3

Now, replace $x$ with $-x$ in the function $f(x)$ .
$g(x) = |6(-x)| -2$

STEP 4

implify the function $g(x)$ .
$g(x) = |-6x| -2$

STEP 5

The absolute value of a negative number is the same as the absolute value of the positive of that number. Therefore, $|-x|$ is the same as $|x|$ .
So, we can simplify $g(x)$ further.
$g(x) = |x| -2$ The function $g(x)$ represents the reflection of the function $f(x)$ in the $y$ -axis.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms