Question

15
what is the domain, range, intervals of increase and decrease for this graph? write using interval notation (no inequalities or variables).

Explanation:

Step1: Identify domain (x-values)

The graph has closed dots at $x=-5$ and $x=4$, so all x-values between these are included.
Domain: $[-5, 4]$

Step2: Identify range (y-values)

The lowest y-value is $-3$, highest is $3$, so all y-values between these are included.
Range: $[-3, 3]$

Step3: Find increasing intervals

The graph rises from $x=-3$ to $x=0$, and from $x=3$ to $x=4$.
Increasing intervals: $(-3, 0), (3, 4)$

Step4: Find decreasing intervals

The graph falls from $x=-5$ to $x=-3$, and from $x=0$ to $x=3$.
Decreasing intervals: $(-5, -3), (0, 3)$

Answer:

Domain: $[-5, 4]$
Range: $[-3, 3]$
Intervals of increase: $(-3, 0), (3, 4)$
Intervals of decrease: $(-5, -3), (0, 3)$