Question

For each prompt that follows, sketch a possible graph of a function on the interval –3 < x < 3 that satisfies the stated properties. a. y = f(x) such that f is increasing on–3 < x <3, concave up on -3

Answer 1

To sketch a graph of a function that satisfies the given properties, the function should be increasing on the interval -3 < x < 3 and concave up at x = -3. The function y = x² satisfies these properties.

Step-by-step explanation:

To sketch a graph of a function that satisfies the given properties, we can start by considering the behavior of the function at specific points. The function should be increasing on the interval -3 < x < 3, which means that as x increases, the corresponding y-values should also increase. Additionally, the function should be concave up at x = -3, which means that the slope should be increasing at that point.

Based on these properties, the function y = x² seems to be a good option. When x is between -3 and 3, the function is increasing, and at x = -3, the function has positive slope that is increasing. The graph of y = x² satisfies all the given properties.

Therefore, option b. y = x² could correspond to the function f(x).