Question: Using the given graph of the function \( f \), find the following. (a) the intercepts, if any…

Using the given graph of the function \( f \), find the following.

(a) the intercepts, if any (b) its domain and range (c) the intervals on which it is increasing, decreasing, or constant (d) whether it is even, odd, or neither

(Type your answer in interval notation. Use a comma to separate answers as needed.)

B. The graph is not decreasing on any interval.

On which interval(s) is the graph constant? Select the correct choice below and fill in any answer boxes within your choice.

A. The graph is constant on

(Type your answer in interval notation. Use a comma to separate answers as needed.)

B. The graph is not constant on any interval.

(d) The function is

Solution

Based on the given graph, let’s answer the questions. (a) Intercepts: The graph intersects the y-axis at \( y = 2 \). It intersects the x-axis at \( x = -2 \), \( x = 0 \), and \( x = 2 \). (b) Domain and Range: - Domain: The graph extends from \( x = -3 \) to \( x = 3 \). - Range: The values of \( y \) range from 0 to 3. Domain: \([-3, 3]\) Range: \([0, 3]\) (c) Intervals: - Increasing: From \( x = -3 \) to \( x = -2 \) and from \( x = 0 \) to \( x = 1 \). - Decreasing: From \( x = -1 \) to \( x = 0 \) and from \( x = 2 \) to \( x = 3 \). - Constant: From \( x = -2 \) to \( x = -1 \) and from \( x = 1 \) to \( x = 2 \). Increasing: \((-3, -2) \cup (0, 1)\) Decreasing: \((-1, 0) \cup (2, 3)\) Constant: \((-2, -1) \cup (1, 2)\) (d) Even, Odd, or Neither: The function is neither even nor odd because it is not symmetric about the y-axis or the origin.