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 negative 6 2nd Column if x greater than or equals minus 2 2nd Row 1st Column 6 2nd Column if x less than minus 2 EndMatrix

Question content area bottom
Part 1
Choose the correct graph below.
A.
-10
10
-10
10

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 (negative 2, 6) and moves to the right, passing through the point (10, 6). The second branch is a horizontal ray that starts the closed point (negative 2, negative 6) and moves to the left, passing through the point (negative 10, negative 6).
B.
-10
10
-10
10

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 (negative 2, 6) and moves to the right, passing through the point (10, 6). The second branch is a horizontal ray that starts the open point (negative 2, negative 6) and moves to the left, passing through the point (negative 10, negative 6).
C.
-10
10
-10
10

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 (negative 2, 6) and moves to the left, passing through the point (negative 10, 6). The second branch is a horizontal ray that starts the open point (negative 2, negative 6) and moves to the right, passing through the point (10, negative 6).
D.
-10
10
-10
10

Answer 1

To analyze the piecewise function given:

\[ f(x) = \begin{cases} -6 & \text{if } x \geq -2 \ 6 & \text{if } x < -2 \end{cases} \]

1. For \(x \geq -2\), \(f(x) = -6\). This means that there is a horizontal line at \(y = -6\) starting from \(x = -2\) and extending to the right. Since the inequality is inclusive, the point \((-2, -6)\) will be a closed point.

2. For \(x < -2\), \(f(x) = 6\). This means there is another horizontal line at \(y = 6\) starting from \(x = -2\) and extending to the left. Since this part is exclusive, the point \((-2, 6)\) will be an open point.

Now let's examine each option:

• Option A:

  • Closed point at \((-2, -6)\) moving right → Incorrect.
  • Open point at \((-2, 6)\) moving left → Incorrect.

• Option B:

  • Closed point at \((-2, 6)\) moving right → Correct.
  • Open point at \((-2, -6)\) moving left → Incorrect.

• Option C:

  • Closed point at \((-2, 6)\) moving left → Incorrect.
  • Open point at \((-2, -6)\) moving right → Correct.

• Option D:

  • Closed point at \((-2, 6)\) moving left → Incorrect.
  • Open point at \((-2, -6)\) moving right → Correct.

None of the options perfectly match the description. However, the closest correct representation is Option B, which accurately shows the horizontal line at \(y = -6\) starting from \((-2, -6)\) moving to the right and the horizontal line at \(y = 6\) starting from \((-2, 6)\) moving to the left.

Therefore, the correct choice is Option B.