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 and the range of the function. b. The intercepts, if any. c. The intervals on which the function is increasing, is decreasing, or is constant. d. Whether the function is even, odd, or neither.

a. What is the domain of the function? \[ [-3, 6] \] (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. (Use a comma to separate answers as needed) B. There is no x-intercept.

Solution

a. What is the domain of the function? The domain of the function is the set of all possible input values (x-values). From the graph, the function starts at \( x = -3 \) and ends at \( x = 6 \). Domain: \([-3, 6]\) What is the range of the function? The range of the function is the set of all possible output values (y-values). From the graph, the lowest value is \( y = -2 \) and the highest value is \( y = 1 \). Range: \([-2, 1]\) b. Determine the x-intercept(s) of the function, if any. The x-intercept occurs where the graph crosses the x-axis. From the graph, it crosses at \( x = -2 \). Therefore, the x-intercept is \( x = -2 \).