Question

the graph represents a cubic function. what does the graph indicate about the values of the function for values of x between 0 and 3?

the values increase throughout the interval.

the values decrease at a constant rate from x = 0 to x ≈ 1, then increase at a constant rate for values of x such that 1 < x < 3.

the function has a local minimum at x ≈ 1.

the function has an absolute minimum at at x ≈ 1.

Explanation:

Step1: Analyze function behavior

A local minimum is a point where the function changes from decreasing to increasing. An absolute minimum is the lowest point on the entire graph. Since the graph has a local minimum at \(x\approx1\) (not an absolute minimum as the function continues to decrease further left), and the function does not increase throughout the interval (it has a decreasing - increasing - decreasing pattern). Also, the rate of change is not constant. But for \(1 < x<3\), the function is decreasing.

Answer:

The values decrease at a constant rate from \(x = 0\) to \(x\approx1\), then increase at a constant rate for values of \(x\) such that \(1 < x<3\).