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

What are the y-intercepts? Select the correct choice below and fill in any answer boxes within your choice.

A. The y-intercept(s) is (are) \(\boxed{\quad}\). (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

B. There are no y-intercepts.

(b) The domain is \(\boxed{\quad}\). (Type your answer in interval notation.)

The range is \(\boxed{\quad}\). (Type your answer in interval notation.)

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

A. The graph is increasing on the interval(s) \(\boxed{\quad}\). (Type your answer in interval notation. Use a comma to separate answers as needed.)

B. The graph is not increasing on any interval.

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Solution

Given the graph of the function \( f \), let’s find the requested information: (a) Y-intercepts: The graph intersects the y-axis at \( y = 1 \). The y-intercept is: \[ 1 \] (b) Domain and Range: - The domain is the set of all x-values for which the function is defined. From the graph, the domain is: \[ [-2, 2] \] - The range is the set of all y-values that the function can take. From the graph, the range is: \[ [1, 2] \] (c) Intervals of Increase/Decrease: - The graph is increasing on the interval: \[ (0, 1) \] - It is decreasing on the intervals: \[ (-2, -1) \] and \[ (1, 2) \] (d) Even, Odd, or Neither: - A function is even if it is symmetric about the y-axis. - A function is odd if it is symmetric about the origin. Since the graph is not symmetric about the y-axis or the origin, the function is neither even nor odd.