Sketch the graph of the function using a window that gives a complete graph.

Question

​f(x)equalsleft brace Start 2 By 2 Matrix 1st Row 1st Column 4 2nd Column if x greater than or equals 0 2nd Row 1st Column negative 4 2nd Column if x less than 0 EndMatrix

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Part 1
Choose the correct graph below.
A.
-10
10
-10
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A coordinate system has a horizontal axis labeled from negative 10 to 10 in increments of 2 and a vertical axis labeled from negative 10 to 10 in increments of 2. A graph has two branches. The first branch is a horizontal ray that startes at the closed point (0, negative 4) and moves to the left, passing through the point (negative 10, negative 4). The second branch is a horizontal ray that starts the open point (0, 4) and moves to the right, passing through the point (10, 4).
B.
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A coordinate system has a horizontal axis labeled from negative 10 to 10 in increments of 2 and a vertical axis labeled from negative 10 to 10 in increments of 2. A graph has two branches. The first branch is a horizontal ray that startes at the open point (0, negative 4) and moves to the left, passing through the point (negative 10, negative 4). The second branch is a horizontal ray that starts the closed point (0, 4) and moves to the right, passing through the point (10, 4).
C.
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A coordinate system has a horizontal axis labeled from negative 10 to 10 in increments of 2 and a vertical axis labeled from negative 10 to 10 in increments of 2. A graph has two branches. The first branch is a horizontal ray that startes at the closed point (0, negative 4) and moves to the right, passing through the point (10, negative 4). The second branch is a horizontal ray that starts the open point (0, 4) and moves to the left, passing through the point (negative 10, 4).
D.
-10
10
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Answer 1

The function you provided is a piecewise function defined as follows:

• For \( x \geq 0 \), \( f(x) = 4 \)
• For \( x < 0 \), \( f(x) = -4 \)

This means:

• When \( x \) is greater than or equal to 0, the function outputs a constant value of 4 (a horizontal line).
• When \( x \) is less than 0, the function outputs a constant value of -4 (another horizontal line).

Now, analyzing the characteristics of these branches:

1. The first piece (for \( x \geq 0 \)) begins at \( (0, 4) \) and goes to the right indefinitely. Since it is defined for \( x \geq 0 \), the point \( (0, 4) \) is included (closed point).

2. The second piece (for \( x < 0 \)) starts from the right at \( (0, -4) \) and extends to the left indefinitely. The point \( (0, -4) \) is also included in this piecewise definition.

Given this information, let's analyze the options provided.

• Option A describes the graph correctly: It indicates that there is a closed point at \( (0, -4) \) and the horizontal ray extends to the left, while there is also a horizontal ray starting at \( (0, 4) \) extending to the right.

• Option B incorrectly describes the left ray as starting from an open point at \( (0, -4) \).

• Option C incorrectly describes the left ray as extending to the right.

• Option D incorrectly describes the left ray as starting from the closed point and extending to the right, which is not correct.

Therefore, the correct graph is Option A.