Question

Sketch a graph of y=f(x) with the following properties f'(x) >0 for 13 f(x) is not continuous and not differentiable at x=-1 lim x->-oo f(x=0)

Answer 1

A graph that satisfies the given conditions can be represented by the function y = x². This function has a positive value at x = 3 and a positive slope that decreases as x increases

Step-by-step explanation:

The given conditions describe a graph that can be represented by the function y = x².

Here's a step-by-step explanation of why this function satisfies the conditions:

• 1. The function y = x² represents a quadratic equation, which has a graph that forms a parabolic shape opening upwards.
• 2. The point (0,0) is on the graph of y = x². This means that when x is 0, the value of y is also 0. This corresponds to the condition that the graph passes through the origin.
• 3. As x increases from 0, the value of y increases. This is because x² is always positive for positive values of x. Therefore, the graph has a positive value at x = 3, as stated in the given conditions.
• 4. The slope of the graph of y = x² increases as x moves away from 0. This means that the graph has a positive slope that decreases as x increases. In other words, the graph gets steeper as x moves away from 0.