Question: The graph of a function is given to the right. Use the graph to find each of the following: a. The…

The graph of a function is given to the right. Use the graph to find each of the following: a. The domain of the function; b. The intercepts, if any; c. The intervals on which the function is increasing, decreasing, or is constant; d. Whether the function is even, odd, or neither.

a. What is the domain of the function? \([-2, 5]\) (Type your answer in interval notation.)

What is the range of the function? \([-2, 1]\) (Type your answer in interval notation.)

b. Determine the x-intercept(s) of the function, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \(-1\) (Use a comma to separate answers as needed) B. There is no x-intercept.

Answer: A. \(-1\)

Solution

The graph of a function is provided, and several questions are asked about it. Here’s the breakdown: a. What is the domain of the function? - The domain is the set of all possible input values (x-values) for the function. - From the graph, the domain is \([-2, 5]\). What is the range of the function? - The range is the set of all possible output values (y-values) for the function. - From the graph, the range is \([-2, 1]\). b. Determine the x-intercept(s) of the function, if any. - The x-intercept is where the function crosses the x-axis (y = 0). - Based on the image, the x-intercept is at \(x = -1\). So, the answer for b is option A: \(-1\).