Mathematics, 12.11.2019 08:31, Thania3902

Find the average rate of change f(x) = 3x + 2
x = 2, x = 5

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Answers

Answered: savthespice

4 explanation: is the greatest common factor

Answered: brandydailey24pe8r24

the average rate of change is 4.

Step-by-step explanation:

The average rate of change is the slope. Therefore, you must use the following formula for calculate the slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

As you can see in the table, when x=5, y=-2 and when x=9, y=14. Then the points you must substitute into the formula are:

(5,-2) and (9,14)

Then, you obtain:

$m=\frac{14-(-2)}{9-5}=4$

Answered: jashart95

Step-by-step explanation:

Substitute the equation and values into the average rate of change formula.

Answered: froyg1234

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2-3x-4\qquad \begin{cases} x_1=-1\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(-1)}{3-(-1)} \\\\\\ \cfrac{[(3)^2-3(3)-4]~~-~~[(-1)^2-3(-1)-4]}{3+1} \\\\\\ \cfrac{[-4]~~-~~[1+3-4]}{4}\implies \cfrac{[-4]-[0]}{4}\implies -1$

Answered: coollid876

Average rate of change = 2

Step-by-step explanation:

We need to find the average rate of change of f(x) over the interval [-4,-1], so first we need to find the end points at x=-4 and x=-1.

From graph we see that y=-3 when x=-4, So the point is (-4,-3)

From graph we see that y=3 when x=-1, So the point is (-1,3)

Now we can plug these points into average rate of change formula:

$Average\ rate=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

where (a,f(a)) and (b,f(b)) are the given points.

$Average\ rate=\frac{-3-3}{-4-\left(-1\right)}$

$Average\ rate=\frac{-3-3}{-4+1}$

$Average\ rate=\frac{-6}{-3}$

$Average\ rate=2$

Hence final answer is 2.

Answered: thezbell

Option 1 is correct.

2 is the average rate of change f(x), represented by the graph, over the interval [0,2]

Step-by-step explanation:

The average rate of change A(x) of f(x) over the interval [a, b] is given by:

$A(x) = \frac{f(b)-f(a)}{b-a}$ .....[1]

As per the statement:

Since, the parabolic graph represents the function f(x) as shown in figure.

We have to find the average rate of change f(x), represented by the graph, over the interval [0,2]

At x = 0

From the graph, we have

f(x) = 4

At x = 2

⇒f(x) = 8

Substitute these given values in [1] we have;

$A(x) = \frac{f(2)-f(0)}{2-0}$

⇒ $A(x) = \frac{8-4}{2-0}$

⇒ $A(x) = \frac{4}{2} = 2$

Therefore, the average rate of change f(x), represented by the graph, over the interval [0,2] is, 2

Answered: loganparrish5370

the average rate of change is equal to

Step-by-step explanation:

Step 1

Find the value of f(x) for x=0

f(0)=4 ------> see the graph

Step 2

Find the value of f(x) for x=2

f(2)=8 ------> see the graph

Step 3

Find the average rate of change f(x)

we know that

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

f(a)=f(0)=4

f(b)=f(2)=8

a=0

b=2

Substitute the values

$\frac{8-4}{2-0}=2$

Answered: Jasminanai42

The rate of change of the given function at [-1,3] is 5

Further explanation:

Given function is:

f(x) = 4x^2-3x-4

And the interval is:

[-1,3]

In order to find the rate of chnage of function the given function's value is calculated at both points and divided by their difference

The formula is:

$Rate\ of\ change= \frac{f(x_2)-f(x_1)}{x_2-x_1}$

Here,

x_1 = -1

x_2 = 3

So,

$f(-1) = 4(-1)^2-3(-1)-4\\=4(1) +3-4\\=4-1\\=3\\f(3) = 4(3)^2-3(3)-4\\= 4(9)-9-4\\=36-13\\=23$

Putting the values in the rate of change formula:

$Rate\ of\ change= \frac{23-3}{3-(-1)}\\= \frac{23-3}{3+1}\\=\frac{20}{4} \\=5$

The rate of change of the given function at [-1,3] is 5

Keywords: Rate of change, functions

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Answered: luap6897

Thank you for posting your question here at I hope the answer will help you. Feel free to ask more questions.

the average rate of change f(x) from x=1 to x=4 represent is The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.

Answered: lace64

The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds. The vertical increase from x = 1 to x = 4, on the y(i.e. f(x))-axis, represents an increase in the height of the water, since f(x) represents the height, in feet, of the water from the fountain at different times. Graph included below.
Water coming out from a fountain is modeled by the function f(x)=-x^2+8x+2 where f(x) represents the