question\ndetermine the interval(s) for which the function shown below is increasing.
question\ndetermine the interval(s) for which the function shown below is increasing.
Answer
Answer:
The function is increasing on the intervals $(-4,-1)$ and $(3,8)$.
Explanation:
Step1: Recall increasing - function definition
A function $y = f(x)$ is increasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, we have $f(x_1)<f(x_2)$.
Step2: Analyze the graph
Looking at the graph, as we move from left - to - right, the $y$ - values of the function are getting larger on the intervals where the graph is going up. We can see that the graph is going up from $x=-4$ to $x = - 1$ and from $x = 3$ to $x=8$. So the intervals where the function is increasing are $(-4,-1)$ and $(3,8)$.