Let's analyze the graph and answer a common **step-by-step question** using your details. --- ## Step-by-Step Solution ### 1. **Identify the Domain** - **Left endpoint:** At \( x = -5 \), the function is defined and \( y = 9 \) (solid dot). - **Right endpoint:** At \( x = 2 \), there is a hole (open circle) at \( (2, 4) \). So, \( x = 2 \) is **not included**. **Domain:** \[ -5 \leq x < 2 \] --- ### 2. **Identify the Range** - **Minimum Value:** At \( (-2, 0) \), the function reaches its lowest point, so the minimum \( y = 0 \). - **Maximum Value:** At \( (-5, 9) \), left endpoint, so the maximum \( y = 9 \). - **Right endpoint:** At \( x = 2 \), there is a hole at \( y = 4 \), so \( y = 4 \) is **not included** at \( x = 2 \). But as \( x \) approaches 2 from the left, \( y \) approaches 4, so all values between 0 and 9 are reached except possibly \( y = 4 \) at \( x = 2 \). **Range:** \[ 0 \leq y \leq 9 \] But since \( y = 4 \) at \( x = 2 \) is a hole, and unless the graph "skips" \( y = 4 \) elsewhere, the value \( 4 \) **is included** at other \( x \) values (observe the curve passes through \( y = 4 \) at other \( x \)). Thus, the **range** is: \[ 0 \leq y \leq 9 \] --- ### 3. **Minimum and Maximum Values** - **Minimum value:** \( 0 \) at \( x = -2 \) - **Maximum value:** \( 9 \) at \( x = -5 \) --- ### 4. **Type of Endpoint at \( x = 2 \)** - **Hole** (open circle) at \( (2, 4) \), so the function is **not defined** at \( x = 2 \). --- ## **Final Answers** **Domain:** \[ [-5, 2) \] **Range:** \[ [0, 9] \] **Minimum value:** \[ 0 \text{ at } x = -2 \] **Maximum value:** \[ 9 \text{ at } x = -5 \] **The function is not defined at \( x = 2 \) (hole at } (2, 4))** --- **If you have a specific question (increasing/decreasing intervals, etc.), please specify!**