Question

I SUCK AT MATH PLEASE HELP

Let f(x)=−3√x .


What is the average rate of change of f(x) from 8 to 64?


A) 28


B) −128


C) 128


D) −28

The table shows the values of a function f(x).


What is the average rate of change of f(x) from −2 to 2?


x f(x)

​ −2 ​ 25

​ −1 ​ 24

0 21

1 16

2 9

3 0


Enter your answer in the box.


The attendance for several baseball games is shown in the table.


Which answer describes the average rate of change from game 2 to game 5?

Game Attendance (number of people)

1 654

2 680

3 702

4 732

5 755


A) The attendance increased by an average of 25 people per game from game 2 to game 5.


B) The attendance increased by an average of 101 people per game from game 2 to game 5.


C) The attendance increased by an average of 19 people per game from game 2 to game 5.


D) The attendance increased by an average of 75 people per game from game 2 to game 5.


What is the average rate of change from −1 to 1 of the function represented by the graph?


An inverse variation function graphed on a coordinate plane. The horizontal x-axis ranges from negative 2 to 2 in increments of 1. The vertical y-axis ranges from negative 2 to 2 in increments of 1. Moving from left to right, the branch is in the third quadrant and passes through begin ordered pair negative 2 comma negative 0.2, begin ordered pair negative 1 comma negative 0.25 end ordered pair, begin ordered pair 0 comma negative 0.33 end ordered pair, begin ordered pair 1 comma negative 0.5 end ordered pair and begin ordered pair 2 comma negative 1 end ordered pair.


Enter your answer in the box.

Answer 1

1. -1/28

2. -4

3.A) The attendance increased by an average of 25 people per game from game 2 to game 5.

4. -.125

Explanation:

To find the rate of change, we use the formula

f(x2) - f(x1)

--------------

x2-x1

1.

f(x) = -(x) ^ 1/3

f(64) = -(64) ^ 1/3 = -4

f(8) =- (8)^1/3 = -2

f(64) - f(8) -4--2 -4+2 -2 -1

-------------- = --------- = ------------- = ----------- = ------

64 - 8 56 56 56 28

2.

f(2) = 9

f(-2) = 25

f(x2) - f(x1) f(2) - f(-2) 9-25 -16 -16

-------------- =----------- = ----------------- = ---------- = ----------- = -4

x2-x1 2--2 2+2 4 4

3.

f(5) = 755

f(2) = 680

f(x2) - f(x1) f(5) - f(2) 755-680 75

-------------- = ---------- = -------------- = ---------- = 25

x2-x1 5-2 3 3

A) The attendance increased by an average of 25 people per game from game 2 to game 5.

4.

f(-1) = -.25

f(1) = -.5

f(x2) - f(x1) f(1) - f(-1) -.5 --.25 -.5+.25 -.25

-------------- = ---------- = -------------- = ---------- = --------- = -.125

x2-x1 1--1 1+1 2 2

Answer 2

Answer with explanation:

We know that average of a function from x=a to x=b is calculated by:

`(f(b)-f(a))/(b-a)`

Ques 1)

`f(x)=-\sqrt[3]{x}`

`f(8)=-\sqrt[3]{8}\\ \\f(8)=-2`

and

`f(64)=-\sqrt[3]{64}\\ \\f(64)=-4`

Hence, the rate of change from 8 to 64 is given by:

`=(-4+2)/(64-8)\\\\=(-2)/(56)\\\\=(-1)/(28)`

Hence, the rate of change is:

`(-1)/(28)`

Ques 2)

The table is given as:

x f(x)

​-2 ​ 25

​-1 ​ 24

0 21

1 16

2 9

3 0

Hence, the average rate of change from -2 to 2 is calculated as:

`=(f(2)-f(-2))/(2-(-2))\\\\\\=(9-25)/(4)\\\\=(-16)/(4)\\\\=-4`

Hence, average rate of change is:

`-4`

Ques 3)

Game Attendance (number of people)

1 654

2 680

3 702

4 732

5 755

The average rate of change from game 2 to game 5 is calculated as:

`=(755-680)/(5-2)\\\\\\=(75)/(3)\\\\=25`

Hence, option: A is the correct answer.

A) The attendance increased by an average of 25 people per game from game 2 to game 5.

Ques 4)

We are asked to find the average rate of change from -1 to 1.

We have the x and y value as follows:

x y=f(x)

-2 -0.2

-1 -0.25

0 -0.33

1 -0.5

2 -1

Hence, the average rate of change from x= -1 to x=1 is calculated as:

`=(f(1)-f(-1))/(1-(-1))\\\\\\=(-0.5-(-0.25))/(1+1)\\\\\\=(-0.25)/(2)\\\\=-0.125`

Hence, the average rate of change from x=-1 to x=1 is:

`-0.125`