Question

the graph of ( f ) is given below. use the graph to answer the following questions:
a) the turning points of the graph are at which ordered pairs? please separate the ordered pairs by commas.
the turning points are at
b) the next part of this question will have you identify relative maximums and minimums. if the function does not have a relative max or min, please answer no solution.
the ( x )-value(s) at which the function has a relative maximum is/are
one or more solutions:
no solution
the relative maximum/maxima are:
one or more solutions:
no solution
the ( x )-value(s) at which the function has a relative minimum is/are:
one or more solutions:
no solution
the relative minimum/minima are:
one or more solutions:
no solution

Explanation:

Step1: Identify turning points

Turning points are points where the function changes direction. From the graph, we can see the turning points are \((-1,5)\), \((4,-3)\), \((7,5)\)

Step2: Identify \(x -\)values for relative maxima

Relative maxima occur at the peaks of the function. The \(x -\)values at the peaks are \(x=-1\) and \(x = 7\)

Step3: Identify relative maxima values

The \(y -\)values at the peaks (relative maxima) are \(y = 5\) (at \(x=-1\)) and \(y = 5\) (at \(x = 7\))

Step4: Identify \(x -\)values for relative minima

Relative minima occur at the trough of the function. The \(x -\)value at the trough is \(x = 4\)

Step5: Identify relative minima value

The \(y -\)value at the trough (relative minima) is \(y=-3\)

Answer:

A) The turning points are at \((-1,5),(4,-3),(7,5)\)

B)

• The \(x -\)value(s) at which the function has a relative maximum is/are \(-1,7\)
• The relative maximum/maxima are \(5,5\)
• The \(x -\)value(s) at which the function has a relative minimum is/are \(4\)
• The relative minimum/minima are \(-3\)