Determine the net change and average rate of change between the values of the variable

Question

A function is given

g(x)=7/x ; x=1, x=a

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

Answer 1

The net change is the absolute value of the difference between g(1) and g(a) which is 7-7/a now add these and you get (7a-7)/a This is sy

The average rate of change or dy/dx is [(7a-7)/a] / a. (The distance from x to a is just a)

This equals (7a-7)/a^2

Answer 2

Hi Nick! Given g(x) = 7/x, we know that g(1)= 7/1 = 7. Likewise, g(a) = 7/a.

The Net change of a function looks at how much the function values, or the y-values, change. Between the two here, the net change is just g(a) - g(1) = 7/a - 7.

The Average change of a function takes into account how much the independent variable, x in this case, changes also, so the function for average change is what we use for slope: (change in y)/(change in x). In this case, [g(a) - g(1)] / (a - 1). Plugging in our net change, it looks like this: (7/a - 7) / (a-1).

If your teacher prefers, you can change that around to make it one fraction instead of two (a "complex fraction" is a fraction within a fraction), then you have (7-7a) / (a(a-1)).

I hope that helps!

Have fun mathing, and let me know if you have any more questions,

Liz Z.