Question

A. What is the average rate of change of the function g(x) = 2x - 7 between the points (-2, -11) and (5, 3)? _________ B. Use the following graphs to answer this part: - which of the above graphs is the graph of g(x)? ______ - over what intervals is g(x) increasing? ________ -- over what intervals is g(x) decreasing? ________

Answer 1

Part A.

To find the average rate of change, we must divide the change in y-values by the change in x-values. Then, by means of the given points, we have

`\text{ rate of change: }(y_2-y_1)/(x_2-x_1)=(3-(-11))/(5-(-2))=(14)/(7)=2`

as we can note the rate of change must be equal to the slope of the given line equation, which is the coefficient of the variable x.

Part B

Lets graph the given equation.

By comparing with the given options, the answer is option C.

On the other hand, the function g(x) is defined for all real numbers, then (as we can see on the picture) function is increasing over all real numvbers. Then, the function increases on the interval:

`x\in(-\infty,\infty)`

The behavior of a line is always the same, this means that the function never decreases. Therefore, the answer to the last question is: None (the function never decreases)