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.

Question

caozeyuan · Answer

rate of chane is slope, since slope is 2, that's your answer

photon336 · Answer

evaluate f(x) at x = 0 and x = 3 and then maybe use the slope formula. 

$$\frac{ y_{2}-y_{1} }{ x_{2}-x_{1} } = m_{average}$$

caozeyuan · Answer

rate of change is dy/dx, this is linear, so it is just the slope

barrelracing · Answer

so I'm confused how do I find the average rate of change

caozeyuan · Answer

look at the slope

caozeyuan · Answer

rate of change gets complicated beyond linear, but this is linear so no worry

photon336 · Answer

first find what the y values are. 

$$f(0) = 2(0)+1 = 1 $$

$$f(3) = 2(3)+1 =  7 $$ 

0,1 

and 

3,7 

since it's just a line you can use the slope formula 

$$m = \frac{ y_{2}-y_{1} }{ x_{2}-x_{1}}$$

then use the formula above to find the slope between those two points and that's the average rate of change.

you could use derivatives too.

photon336 · Answer

$$y_{2} = 7, y_{1} = 1, x_{2}  = 3, x_{1} =  0   $$

$$\frac{ 7-1 }{ 3-0 } = \frac{ 6 }{ 3 } $$

photon336 · Answer

since it's a line you could avoid all this and just do what @caozeyuan said but that's if you haven't learned derivatives yet but that's just a technical term for slope.

barrelracing · Answer

thank u both.

photon336 · Answer

@Barrelracing if you wanted you could take the derivative

photon336 · Answer

$$y = m(x) + b$$

$$\frac{ dY }{ dx } = m $$

barrelracing · Answer

well didn't u just provide the answer?

photon336 · Answer

in case you wanted a faster way to do it

photon336 · Answer

$$\frac{ dY }{ dX }, 2x+1 =  2x ^{1-1} = 2x ^{0} = 2$$