Question

1) If g(x) is a linear function, g(-2) = 6 and g(2) = 18, what is the rate of change? Is this function increasing or decreasing? Show your work!

Answer 1

Answers:

Rate of change = 3

The function is increasing

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Step-by-step explanation:

The notation g(-2) = 6 means the input x = -2 leads to the output y = 6. Therefore, the point (-2,6) is on f(x). The other point given is (2,18).

For linear functions, the terms "rate of change" and "slope" are the same thing.

Let's use the slope formula on the two points (-2,6) and (2,18)

`(x_1,y_1) = (-2,6) \text{ and } (x_2,y_2) = (2,18)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (18 - 6)/(2 - (-2))\\\\m = (18 - 6)/(2 + 2)\\\\m = (12)/(4)\\\\m = 3\\\\`

The slope is 3, which can be written as 3/1

A slope of 3/1 means we go up 3 and to the right 1.

slope = rise/run = 3/1

rise = 3 = go up 3

run = 1 = go to the right 1

Since the slope is positive, this means the line is going uphill as we move to the right. In other words, the function is increasing.