Question

the graph of a function is shown.
which point is a good approximation of a relative maximum of the graph?
(1,3)
(2,0)
(-2,0)
(-1,-3)

Explanation:

Step1: Recall the definition of a relative maximum

A relative maximum is a point on the graph where the function changes from increasing to decreasing.

Step2: Analyze each point

• For \((2,0)\) and \((- 2,0)\): These are \(x -\)intercepts (where \(y = 0\)), not relative maxima.
• For \((-1,-3)\): This is a low - point (a relative minimum as the function changes from decreasing to increasing around it).
• For \((1,3)\): Looking at the graph, near \(x = 1\), the function changes from increasing (to the left of \(x = 1\)) to decreasing (to the right of \(x = 1\)).

Answer:

\((1,3)\)