Question

for the function graphed, give the minimum and maximum values of ( f(x) ) and the ( x )-values at which they occur. find the maximum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. the function has a maximum value of ( square ) at ( x=square ). b. the function does not have a maximum value.

Explanation:

Step1: Analyze the graph for maximum value

Look for the highest point on the graph. The \( y - \)coordinate of this point is the maximum value of \( f(x) \), and the \( x - \)coordinate is the \( x - \)value at which the maximum occurs.
From the graph, the highest point has \( y = 5 \) and \( x=-4 \).

Step2: Analyze the graph for minimum value

Look for the lowest point on the graph. The \( y - \)coordinate of this point is the minimum value of \( f(x) \), and the \( x - \)coordinate is the \( x - \)value at which the minimum occurs.
From the graph, the lowest point has \( y=-6 \) and \( x = 2 \).

Answer:

For the minimum: The function has a minimum value of \(-6\) at \(x = 2\).
For the maximum (choosing option A): The function has a maximum value of \(5\) at \(x=-4\).