From the given function, we have that:
d. The function is increasing over the intervals (-5,0) and (5,8).
e. The function is decreasing over the intervals (-∞, -5) and (0,5).
f. The rate of change over the interval (-5,0) is of 1.6.
g. The rate of change is of 0 in the interval (-2,3).
h. At x = -2.5, we have that f(-2x) = -2 and 2f(x) = 2.
When a function is increasing, looking at it's graph?
Looking at the graph, we get that a function f(x) is decreasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y decreases.
In this problem, the intervals are:
(-5,0) and (5,8).
When a function is decreasing, looking at it's graph?
Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.
In this problem, the intervals are:
(-∞, -5) and (0,5).
What is the average rate of change of a function?
The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Over the interval from -5 to 0, we have that:
Hence the rate is:
(5 - (-3))/(0 - (-5)) = 1.6.
The rate of change over the interval (-5,0) is of 1.6.
From the graph, we also have that f(-2) = f(3), hence:
The rate of change is of 0 in the interval (-2,3).
At x = -2.5, we have that:
- 2f(x) = 2f(-2.5) = 2(1) = 2.
More can be learned about functions at https://brainly.com/question/24808124
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