use the graph to determine open interval on which the function is increasing, if any. select the correct…
use the graph to determine open interval on which the function is increasing, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function is increasing on the interval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. there is no interval on which the function is increasing.
Answer
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 $f(x_1)<f(x_2)$. Graphically, the function is increasing when the graph rises from left - to - right.
Step2: Analyze the given graph
Looking at the graph of the function, we can see that the function has a vertex at $x=- 1$. To the left of $x = - 1$, the function is decreasing, and to the right of $x=-1$, the function is increasing.
Step3: Write the increasing interval
The function is increasing for $x>-1$. In interval notation, this is the interval $(-1,\infty)$.
Answer:
A. The function is increasing on the interval(s) $(-1,\infty)$