Question

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

Answer 1

@Nnesha

Answer 2

@Ultrilliam

Answer 3

Hold up one sec

Answer 4

Welcome to QC BTW!

Answer 5

f(x) can be written as y \[\huge\rm y=2^x+1\]
first of all we need to find y values that corresponds to x=0,2
substitute x for 0 and 2 to find y

another word for *average rate of change* is *slope *
formula to find slope is \[\large\rm \frac{ y_2-y_1 }{ x_2-x_1}\]

Answer 6

Hey there buddy =) Welcome to QC :) So what we need to do is first use our Formula from when we were in geometry Which is
\[Y_2-Y_1/X_2-X_1\]
This formula is the formula for the average rate of change for two points.
Now what we need to do is use a new formula, Which is now
\[F_b - F_a /b-a\]

Try to use this formula to solve your answer.

Answer 7

\[y=2^x+1\]\[\large\rm \color{Red}{y}=2^\color{blue}{0}+1=1+1\] (anything raised to the zero power is equal to 1

when x =0 y =2
so when x=2 y=what?

Answer 8

how did you get that ?

Answer 9

y=2 when x=0
now replace x with 2 to find the y value when x=2

Answer 10

\[y=2^\color{blue}{x}+1\]\[\large\rm \color{Red}{y}=2^\color{blue}{0}+1\]\[\large\rm \color{Red}{y}=1+1\]\[\large\rm \color{Red}{y}=2\]



repeat the steps. This time replace `x` with `2`

Answer 11

yes correct!
so when x = 0 ,y=2
and when x =2 , y =5
we can write it as order pair `(0,2),(2,5)`
now use the slope formula for the slope \[\large\rm (\color{blue}{x_1} ,\color{red}{y_1})(\color{blue}{x_2},\color{Red}{y_2})\]
\[\large\rm slope=\frac{\color{Red}{ y_2 - y_1} }{\color{blue}{ x_2-x_1} }\]

Answer 12

correct. good job

Answer 13

np

Answer 14

aww thanks for the nice words. appreciate 't!! o^_^o :=))