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2 years ago

the graph of f(x)=2^x+1 is shown below explain how to find the average rate of change between x=1 and x=3

Mathematics

1 answer:

max2010maxim [7]2 years ago

8 0

First find the values of f(x) for x = 1 and for x = 3.
Reading off the graph they are f(x) = 3 and f(x) = 9 respectively.
You could also have found thess values by substitution of x in f(x) - eg for x = 1 f(x) = 2^1 + 1 = 3.

Average rate of change = difference in f(x) / difference in x = (9 - 3) / (3 - 1) = 6/2 = 3 answer

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Given :

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$\gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}$

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Let's solve by using midpoint formula :

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$\bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}$

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$\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}$

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$\: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}$

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$\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}$

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$\underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓$

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