Question

given the function in the graph below, identify the intervals on which the function appears to be increasing. choose all that apply. (you can click on a graph to enlarge it.)

Explanation:

Step1: Recall increasing - function definition

A function $y = f(x)$ is increasing on an interval if, as $x$ increases, $y$ also increases. That is, for any two points $x_1$ and $x_2$ in the interval with $x_1

Step2: Analyze the graph

Looking at the graph, we scan from left - to - right. We observe the parts of the curve where it is going up.

Step3: Identify the increasing intervals

We see that the function is increasing in two intervals.

Answer:

Intervals where the function is increasing need to be determined by observing the graph. If we assume the x - axis has markings such that the left - most part of the graph starts at $x = a$, the first increasing interval is from some value $x_1$ to $x_2$ and the second increasing interval is from $x_3$ to $x_4$. Without specific x - values on the graph, we can only describe the process. In general, we would write the intervals in the form $(x_1,x_2)$ and $(x_3,x_4)$ where the function is rising as we move from left to right.