Question

I SUCK AT MATH PLEASE HELP

Answer 1

Answer with explanation:

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

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

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:

$=\dfrac{-4+2}{64-8}\\\\=\dfrac{-2}{56}\\\\=\dfrac{-1}{28}$

Hence, the rate of change is:

           $\dfrac{-1}{28}$

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:

$=\dfrac{f(2)-f(-2)}{2-(-2)}\\\\\\=\dfrac{9-25}{4}\\\\=\dfrac{-16}{4}\\\\=-4$

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:

$=\dfrac{755-680}{5-2}\\\\\\=\dfrac{75}{3}\\\\=25$

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:

  $=\dfrac{f(1)-f(-1)}{1-(-1)}\\\\\\=\dfrac{-0.5-(-0.25)}{1+1}\\\\\\=\dfrac{-0.25}{2}\\\\=-0.125$

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

                              $-0.125$

Answer 2

Answer:

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

Step-by-step 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