Question

WILL GIVE MEDAL PLEASE HELP!

The graph of f(x) = 2x + 1 is shown below.
Explain how to find the average rate of change between x = 0 and x = 3.

Answer 1

@Hero @myininaya

Answer 2

The average rate of change from x=0 to x=3 is going to be the slope of the line from x=0 to x=3.

So we need to find slope :)
Remember your slope formula? \(\large\rm \frac{y_2-y_1}{x_2-x_1}\)
We find out how much the y (height) changed,
divide it by the x change,
and that gives us slope, rise over run.

Our x1 and x2 are clearly x=0 and x=3.
What about y2?
Maybe it's easier if I write the slope formula using function notation :)
Relates better to this problem I guess.

Answer 3

slope:\(\large\rm \frac{f(x_2)-f(x_1)}{x_2-x_1}\)

We know our x's: \(\large\rm \frac{f(3)-f(0)}{3-0}\)

So for our y's, we need to know what the function is equal to when x=0 and when x=3.

So what do you get for f(3)?
\[\large\rm f(\color{orangered}{x})=2^{\color{orangered}{x}}+1\]\[\large\rm f(\color{orangered}{3})=2^{\color{orangered}{3}}+1\]What does that simplify to? :)

Answer 4

F= 9

Answer 5

Good good good.\[\large\rm f(\color{orangered}{x})=2^{\color{orangered}{x}}+1\]\[\large\rm f(\color{orangered}{0})=2^{\color{orangered}{0}}+1\]How bout the other one?

Answer 6

F= 2

Answer 7

\[\large\rm m=\frac{9-2}{3-0}\]Cool! Now find your slope! :D

Answer 8

7/3 ?

Answer 9

Good good good.
The function went up by 7,
over a distance of 3.

So an average rate of change of 7/3.

Yayyyy good job \c:/