Question

1. draw a function with one interval increasing, two intervals decreasing, has a domain of -2,5, a minimum of -3 and a maximum of 4.

Explanation:

Step1: Determine key points

• Domain is \([-2,5]\).
• Minimum value \(y = - 3\), maximum value \(y = 4\).
• One increasing interval, two decreasing intervals.

Step2: Sketch the function

• Start at a point in the domain \([-2,5]\) for the maximum. Let's assume the maximum is at \(x=-2\), so the point is \((-2,4)\).
• Then have a decreasing interval.
• Reach the minimum point. Let's say the minimum is at \(x = 1\), so the point is \((1,-3)\).
• Then have an increasing interval.
• Then have another decreasing interval. Let's end at \(x = 5\). For example, if at \(x = 5\), \(y=0\) (any value within the range of the function).

Answer:

Draw a curve starting at \((-2,4)\), decreasing to \((1,-3)\), then increasing and then decreasing to \((5,0)\) (the exact shape can vary as long as it meets the criteria of one increasing interval, two decreasing intervals, domain \([-2,5]\), minimum \(-3\) and maximum \(4\)).