## anonymous one year ago 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.

1. anonymous

2. anonymous

@Hero @myininaya

3. zepdrix

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.

4. zepdrix

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? :)

5. anonymous

F= 9

6. zepdrix

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?

7. anonymous

F= 2

8. zepdrix

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

9. anonymous

7/3 ?

10. zepdrix

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:/