QuestionGraph the equation $y=-5|x|$ and describe the transformation from $f(x)=|x|$ . Choose the correct option.

Studdy Solution

STEP 1

Assumptions1. The parent function is $f(x)=|x|$ . The transformed function is $y=-5|x|$
3. The transformation involves a reflection and/or a stretch/compression

STEP 2

First, let's graph the parent function $f(x)=|x|$ . This is a V-shaped graph that intersects the origin (0,0) and opens upwards.

STEP 3

Now, let's graph the transformed function $y=-5|x|$ . The negative sign in front of the absolute value function indicates a reflection across the x-axis. The factor of5 indicates a vertical stretch by a factor of5.

STEP 4

To graph $y=-|x|$ , we can start by plotting points. Since the absolute value function is symmetrical about the y-axis, we only need to plot points for x >=0 and then reflect these points across the y-axis.

STEP 5

Let's plot the points for $x=0,1,2,3,4$ .
For $x=0$ , $y=-5|0|=0$ .
For $x=1$ , $y=-5|1|=-5$ .
For $x=2$ , $y=-5|2|=-10$ .
For $x=3$ , $y=-5|3|=-15$ .
For $x=4$ , $y=-5|4|=-20$ .

STEP 6

Now, reflect these points across the y-axis to get the points for $x<0$ .

STEP 7

Finally, connect the plotted points with a straight line to complete the graph of $y=-5|x|$ .

STEP 8

Now, let's describe the transformation from the parent function $f(x)=|x|$ .
The negative sign in front of the absolute value function indicates a reflection across the x-axis. The factor of5 indicates a vertical stretch by a factor of5.
Therefore, the correct answer is A. The parent function $f(x)=|x|$ is vertically stretched and reflected across the $x$ -axis.

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