Solved on Feb 25, 2024

Graph the absolute value function $y = -5|x|$ . Click to plot the vertex.

STEP 1

Assumptions
1. The function to be graphed is $y = -5|x|$ .
2. The graph will be plotted on a standard Cartesian coordinate system.
3. The graph of $|x|$ is a V-shaped graph that opens upwards with its vertex at the origin (0,0).
4. The graph of $-5|x|$ will be a reflection of $|x|$ across the x-axis, scaled by a factor of 5.

STEP 2

Identify the vertex of the function $y = -5|x|$ . Since $|x|$ has a vertex at the origin (0,0), the vertex of $y = -5|x|$ will also be at the origin (0,0).

STEP 3

Plot the vertex on the graph at the point (0,0).

STEP 4

Understand the behavior of the absolute value function. For $x \geq 0$ , $|x| = x$ , and for $x < 0$ , $|x| = -x$ .

STEP 5

For $x \geq 0$ , the function $y = -5|x|$ simplifies to $y = -5x$ . This is a straight line with a slope of -5, passing through the origin.

STEP 6

Plot the line $y = -5x$ for $x \geq 0$ starting from the origin and extending to the right.

STEP 7

For $x < 0$ , the function $y = -5|x|$ simplifies to $y = -5(-x) = 5x$ . This is a straight line with a slope of 5, passing through the origin.

STEP 8

Plot the line $y = 5x$ for $x < 0$ starting from the origin and extending to the left.

STEP 9

The two lines $y = -5x$ for $x \geq 0$ and $y = 5x$ for $x < 0$ together form the V-shaped graph of $y = -5|x|$ , which opens downwards due to the negative sign in front of the 5.

STEP 10

Ensure that the graph is symmetric with respect to the y-axis since the function $y = -5|x|$ is an even function.

STEP 11

The graph is now complete, showing a V-shaped figure with the vertex at the origin (0,0), opening downwards, and with lines that have slopes of -5 and 5 for the right and left sides, respectively.

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Graph the absolute value function $y = -5|x|$ . Click to plot the vertex.

STEP 1

STEP 2

Identify the vertex of the function $y = -5|x|$ . Since $|x|$ has a vertex at the origin (0,0), the vertex of $y = -5|x|$ will also be at the origin (0,0).

STEP 3

Plot the vertex on the graph at the point (0,0).

STEP 4

Understand the behavior of the absolute value function. For $x \geq 0$ , $|x| = x$ , and for $x < 0$ , $|x| = -x$ .

STEP 5

For $x \geq 0$ , the function $y = -5|x|$ simplifies to $y = -5x$ . This is a straight line with a slope of -5, passing through the origin.

STEP 6

Plot the line $y = -5x$ for $x \geq 0$ starting from the origin and extending to the right.

STEP 7

For $x < 0$ , the function $y = -5|x|$ simplifies to $y = -5(-x) = 5x$ . This is a straight line with a slope of 5, passing through the origin.

STEP 8

Plot the line $y = 5x$ for $x < 0$ starting from the origin and extending to the left.

STEP 9

The two lines $y = -5x$ for $x \geq 0$ and $y = 5x$ for $x < 0$ together form the V-shaped graph of $y = -5|x|$ , which opens downwards due to the negative sign in front of the 5.

STEP 10

Ensure that the graph is symmetric with respect to the y-axis since the function $y = -5|x|$ is an even function.

STEP 11

The graph is now complete, showing a V-shaped figure with the vertex at the origin (0,0), opening downwards, and with lines that have slopes of -5 and 5 for the right and left sides, respectively.

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Graph the absolute value function y=−5∣x∣y = -5|x|y=−5∣x∣. Click to plot the vertex.

STEP 1

STEP 2

Identify the vertex of the function y=−5∣x∣ y = -5|x| y=−5∣x∣. Since ∣x∣ |x| ∣x∣ has a vertex at the origin (0,0), the vertex of y=−5∣x∣ y = -5|x| y=−5∣x∣ will also be at the origin (0,0).

STEP 3

Plot the vertex on the graph at the point (0,0).

STEP 4

Understand the behavior of the absolute value function. For x≥0 x \geq 0 x≥0, ∣x∣=x |x| = x ∣x∣=x, and for x<0 x < 0 x<0, ∣x∣=−x |x| = -x ∣x∣=−x.

STEP 5

For x≥0 x \geq 0 x≥0, the function y=−5∣x∣ y = -5|x| y=−5∣x∣ simplifies to y=−5x y = -5x y=−5x. This is a straight line with a slope of -5, passing through the origin.

STEP 6

Plot the line y=−5x y = -5x y=−5x for x≥0 x \geq 0 x≥0 starting from the origin and extending to the right.

STEP 7

For x<0 x < 0 x<0, the function y=−5∣x∣ y = -5|x| y=−5∣x∣ simplifies to y=−5(−x)=5x y = -5(-x) = 5x y=−5(−x)=5x. This is a straight line with a slope of 5, passing through the origin.

STEP 8

Plot the line y=5x y = 5x y=5x for x<0 x < 0 x<0 starting from the origin and extending to the left.

STEP 9

The two lines y=−5x y = -5x y=−5x for x≥0 x \geq 0 x≥0 and y=5x y = 5x y=5x for x<0 x < 0 x<0 together form the V-shaped graph of y=−5∣x∣ y = -5|x| y=−5∣x∣, which opens downwards due to the negative sign in front of the 5.

STEP 10

Ensure that the graph is symmetric with respect to the y-axis since the function y=−5∣x∣ y = -5|x| y=−5∣x∣ is an even function.

STEP 11

The graph is now complete, showing a V-shaped figure with the vertex at the origin (0,0), opening downwards, and with lines that have slopes of -5 and 5 for the right and left sides, respectively.

Start learning now

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

Graph the absolute value function $y = -5|x|$ . Click to plot the vertex.

Identify the vertex of the function $y = -5|x|$ . Since $|x|$ has a vertex at the origin (0,0), the vertex of $y = -5|x|$ will also be at the origin (0,0).

Understand the behavior of the absolute value function. For $x \geq 0$ , $|x| = x$ , and for $x < 0$ , $|x| = -x$ .

For $x \geq 0$ , the function $y = -5|x|$ simplifies to $y = -5x$ . This is a straight line with a slope of -5, passing through the origin.

Plot the line $y = -5x$ for $x \geq 0$ starting from the origin and extending to the right.

For $x < 0$ , the function $y = -5|x|$ simplifies to $y = -5(-x) = 5x$ . This is a straight line with a slope of 5, passing through the origin.

Plot the line $y = 5x$ for $x < 0$ starting from the origin and extending to the left.

The two lines $y = -5x$ for $x \geq 0$ and $y = 5x$ for $x < 0$ together form the V-shaped graph of $y = -5|x|$ , which opens downwards due to the negative sign in front of the 5.

Ensure that the graph is symmetric with respect to the y-axis since the function $y = -5|x|$ is an even function.