Question

select the correct answer. consider the given function. f(x) = \

$$\begin{cases} 5, & x < -2 \\\\ 3, & -2 \\leq x < 0 \\\\ 0, & 0 \\leq x < 2 \\\\ -3, & x \\geq 2 \\end{cases}$$

which graph represents the given function?

Explanation:

Answer:

To sketch the graph:

• For \( x < -2 \), \( f(x) = 5 \): Horizontal line at \( y = 5 \), open circle at \( x = -2 \).
• For \( -2 \leq x < 0 \), \( f(x) = 3 \): Horizontal line at \( y = 3 \), closed circle at \( x = -2 \), open circle at \( x = 0 \).
• For \( 0 \leq x < 2 \), \( f(x) = 0 \): Horizontal line at \( y = 0 \), closed circle at \( x = 0 \), open circle at \( x = 2 \).
• For \( x \geq 2 \), \( f(x) = -3 \): Horizontal line at \( y = -3 \), closed circle at \( x = 2 \).

Label the x-axis (for intervals) and y-axis (for \( y = 5, 3, 0, -3 \)). Plot each segment with correct endpoints (closed for inclusive, open for exclusive).