QuestionA reflection in the $x$ -axis of $y=f(x)$ is $h(x)=$ . A reflection in the $y$ -axis is represented by .

Studdy Solution

STEP 1

Assumptions1. We are working with the function $y=f(x)$ . . A reflection in the $x$ -axis means that the $y$ -values of the function are inverted.
3. A reflection in the $y$ -axis means that the $x$ -values of the function are inverted.

STEP 2

Let's first find the representation of the reflection in the $x$ -axis. This means that the $y$ -values of the function are inverted. Therefore, the new function $h(x)$ will be the negative of the original function $f(x)$ .
$h(x) = -f(x)$

STEP 3

Now let's find the representation of the reflection in the $y$ -axis. This means that the $x$ -values of the function are inverted. Therefore, the new function will be the original function $f(x)$ evaluated at $-x$ .
$f(-x)$ So, a reflection in the $x$ -axis of the graph of $y=f(x)$ is represented by $h(x)=-f(x)$ , while a reflection in the $y$ -axis of the graph of $y=f(x)$ is represented by $f(-x)$ .

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