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2 years ago

Find the average rate of change of the function defined by the following table. x y -2 -5 2 35 6 75 10 115

Mathematics

1 answer:

Pani-rosa [81]2 years ago

6 0

By definition we have that the average rate of change of the function is:

$AVR = \frac{f(x2) - f(x1)}{x2 - x1}$

Evaluating the function for the complete interval we have that the AVR is given by:

$AVR = \frac{115 - (-5)}{10 - (-2)}$

Rewriting we have:

$AVR = \frac{115+5}{10+2}$

Simplifying the expression we have:

$AVR = \frac{120}{12}$

$AVR = 10$

Answer:

the average rate of change of the function defined by the table is:

$AVR = 10$

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2 years ago

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Answer:

1. Alexa traveled at a faster rate because the slope of her line is $\frac{3}{4}$ , which is greater than the slope of the line described by the data in Mia’s table.

Step-by-step explanation:

We know that,

Slope of $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Mia records the distance traveled over the time by the table.

Taking the points (10,5) and (18,9), the slope is given by,

Mia's slope = $\frac{9-5}{18-10}$

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Alexa's slope = $\frac{6-3}{8-4}$

i.e. Alexa's slope = $\frac{3}{4}$

As, Alexa's slope = $\frac{3}{4}$ > $\frac{1}{2}$ = Mia's slope.

So, the correct option is,

1. Alexa traveled at a faster rate because the slope of her line is $\frac{3}{4}$ , which is greater than the slope of the line described by the data in Mia’s table.

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2 years ago

Read 2 more answers

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