Question

select all the intervals where f is increasing.
choose all answers that apply:
a -3 < x < -2
b -1 < x < 0
c 3.5 < x < 4.5
d none of the above

Explanation:

Step1: Recall increasing - function concept

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

Step2: Analyze interval $-3 < x < - 2$

In the interval $-3 < x < - 2$, as we move from left to right (increase $x$), the $y$ - values of the function $y = f(x)$ are decreasing. So the function is not increasing on this interval.

Step3: Analyze interval $-1 < x < 0$

In the interval $-1 < x < 0$, as we move from left to right (increase $x$), the $y$ - values of the function $y = f(x)$ are increasing. So the function is increasing on this interval.

Step4: Analyze interval $3.5 < x < 4.5$

In the interval $3.5 < x < 4.5$, as we move from left to right (increase $x$), the $y$ - values of the function $y = f(x)$ are increasing. So the function is increasing on this interval.

Answer:

B. $-1 < x < 0$, C. $3.5 < x < 4.5$