Let's answer each question step by step using the graph provided. --- ## a) Determine \( f(-2) \) - **Locate \( x = -2 \) on the x-axis.** - **Find the y-coordinate of the graph at \( x = -2 \).** From the graph: At \( x = -2 \), the function \( f(x) \) is at \( y = -1 \). **Final Answer:** \[ f(-2) = -1 \] --- ## b) Determine \( f(3) \) - **Locate \( x = 3 \) on the x-axis.** - **Find the y-coordinate of the graph at \( x = 3 \).** From the graph: At \( x = 3 \), the function \( f(x) \) is at \( y = 2 \). **Final Answer:** \[ f(3) = 2 \] --- ## c) Find all \( x \) for which \( f(x) = -1 \) - **Look for all points where the graph crosses \( y = -1 \).** From the graph: The graph intersects \( y = -1 \) at \( x = -2 \) and \( x = \). **Final Answer:** \[ f(x) = -1 \text{ at } x = -2 \text{ and } x = \] --- ## d) Find all \( x \) for which \( f(x) = -4 \) - **Look for the point(s) where the graph crosses \( y = -4 \).** From the graph: The graph intersects \( y = -4 \) at \( x = 1 \). **Final Answer:** \[ f(x) = -4 \text{ at } x = 1 \] --- ## e) Determine the x-intercept(s) - **These are the points where the graph crosses the x-axis (\( y = \)).** From the graph: The graph crosses the x-axis at \( x = -3 \), \( x = \), and \( x = 2 \). **Final Answer:** \[ \text{x-intercepts: } x = -3,\ ,\ 2 \] --- ## f) Determine the y-intercept - **This is the point where the graph crosses the y-axis (\( x = \)).** From the graph: At \( x = \), the function \( f() = -1 \). **Final Answer:** \[ \text{y-intercept: } y = -1 \] --- ## g) Determine the domain of \( f \) - **The domain is the set of all possible \( x \)-values for which the function is defined.** From the graph: The graph starts at \( x = -4 \) and ends at \( x = 4 \). **Final Answer:** \[ \text{Domain: } [-4, 4] \] --- ## h) Determine the range of \( f \) - **The range is the set of all possible \( y \)-values the function takes.** From the graph: The lowest value is \( y = -4 \) and the highest is \( y = 3 \). **Final Answer:** \[ \text{Range: } [-4, 3] \] --- ### **Summary Table** | Part | Solution | Explanation | |------|------------------|-----------------------------------------------------| | a | \( f(-2) = -1 \) | At \( x = -2 \), graph is at \( y = -1 \) | | b | \( f(3) = 2 \) | At \( x = 3 \), graph is at \( y = 2 \) | | c | \( x = -2, \) | Graph crosses \( y = -1 \) at \( x = -2 \), \( \)| | d | \( x = 1 \) | Graph crosses \( y = -4 \) at \( x = 1 \) | | e | \( x = -3, , 2 \)| Graph crosses x-axis at those x-values | | f | \( y = -1 \) | At \( x = \), \( y = -1 \) | | g | \( [-4, 4] \) | Graph exists between \( x = -4 \) and \( x = 4 \) | | h | \( [-4, 3] \) | \( y \) ranges from \( -4 \) to \( 3 \) |