Question

suppose that the function g is defined as follows.
\\g(x)=\

$$\begin{cases} -2 & \\text{if } -3.5 < x \\leq -2.5 \\\\ -1 & \\text{if } -2.5 < x \\leq -1.5 \\\\ 0 & \\text{if } -1.5 < x < -0.5 \\\\ 1 & \\text{if } -0.5 \\leq x < 0.5 \\\\ 2 & \\text{if } 0.5 \\leq x < 1.5 \\end{cases}$$

\\
graph the function g.

Explanation:

Step1: Analyze the first interval

For \( -3.5 < x \leq -2.5 \), \( g(x) = -2 \). This is a horizontal line segment. We draw a line from \( x = -3.5 \) (open circle, since \( x > -3.5 \)) to \( x = -2.5 \) (closed circle, since \( x \leq -2.5 \)) at \( y = -2 \).

Step2: Analyze the second interval

For \( -2.5 < x \leq -1.5 \), \( g(x) = -1 \). Draw a horizontal line from \( x = -2.5 \) (open circle) to \( x = -1.5 \) (closed circle) at \( y = -1 \).

Step3: Analyze the third interval

For \( -1.5 < x < -0.5 \), \( g(x) = 0 \). Draw a horizontal line from \( x = -1.5 \) (open circle) to \( x = -0.5 \) (open circle) at \( y = 0 \).

Step4: Analyze the fourth interval

For \( -0.5 \leq x < 0.5 \), \( g(x) = 1 \). Draw a horizontal line from \( x = -0.5 \) (closed circle) to \( x = 0.5 \) (open circle) at \( y = 1 \).

Step5: Analyze the fifth interval

For \( 0.5 \leq x < 1.5 \), \( g(x) = 2 \). Draw a horizontal line from \( x = 0.5 \) (closed circle) to \( x = 1.5 \) (open circle) at \( y = 2 \).

Answer:

The graph consists of horizontal line segments:

• From \( (-3.5, -2) \) (open) to \( (-2.5, -2) \) (closed).
• From \( (-2.5, -1) \) (open) to \( (-1.5, -1) \) (closed).
• From \( (-1.5, 0) \) (open) to \( (-0.5, 0) \) (open).
• From \( (-0.5, 1) \) (closed) to \( (0.5, 1) \) (open).
• From \( (0.5, 2) \) (closed) to \( (1.5, 2) \) (open).