Question

The table of values represents a quadratic function.

What is the average rate of change for f(x) from x = −10 to x = 0?

Enter your answer in the box.

______

Answer 1

@Vocaloid

Answer 2

first you need to calculate the amount the function changes

take a look at the table and calculate

f(0) - f(-10) = ?

Answer 3

10f

Answer 4

f(x) means the value of the function at x

f(0) means the value of the function at x = 0

what is f(0)?

Answer 5

0

Answer 6

take a look at the table

what is the value of the function when x = 0?

Answer 7

-6

Answer 8

good, so that means f(0) = -6

using a similar logic, what is f(-10)? you must look at the table to answer this

Answer 9

184

Answer 10

awesome

so the change from f(-10) to f(0) = -6 - 184 = -190

then, we divide that by (0 - (-10)) = 10

so -190/10 = -19 = your answer

Answer 11

Let f(x) = x^2 + 3x − 4.

What is the average rate of change for the quadratic function from x = −3 to x = 8?



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________

Answer 12

the answer is 8

Answer 13

not quite, we use the same process as last time

Answer 14

where a is the first x-value and b is the second x-value

Answer 15

since we want the change from -3 to 8, a = -3 and b = 8

Answer 16

first find f(8)

Answer 17

8f

Answer 18

f(8) = 7

Answer 19

actually nvm I just checked the answer, it's 8

just remember, when I say f(__) something, I don't mean "multiply it by f" I mean find the value of the function at that value

Answer 20

so when I say "find the value of f(8) it doesn't mean multiply 8 by f, it means find the value of the function at x = 8"

Answer 21

so yeah, the final answer is 8

Answer 22

Let f(x) = −1/2(x + 2)^2 + 5 .

What is the average rate of change for the quadratic function from x = −3 to x = 1?



Enter your answer in the box.


______

Answer 23

same thing as before

[ f(1) - f(-3) ] then divide that by 1 - (-3)

remember, f(1) doesn't mean multiply f by 1, it means find the value of the function at x = 1

Answer 24

4f

Answer 25

*** f(1) doesn't mean multiply f by 1;it means find the value of the function at x = 1 ***

Answer 26

with that being said, what is f(1)?

Answer 27

1

Answer 28

*** find the value of the function at x = 1 ***

Answer 29

this is your function

f(x) = −1/2(x + 2)^2 + 5

f(1) means plug in 1 into the function and find the result

Answer 30

f

Answer 31

again, f(1) does not mean multiply f * 1, it means to let x = 1 and plug it into the function

Answer 32

f(x) = −1/2(x + 2)^2 + 5

plug in x = 1 and calculate what f(1) equals

Answer 33

0.5

Answer 34

good, now repeat for f(-3)

Answer 35

4.5

Answer 36

good, so f(1) - f(-3) = ?

use the values of f(1) and f(-3) that we just calculated. the answer is *not* 4f

Answer 37

4

Answer 38

good

now we divide that by (1 - (-3)) = 4

so 4/4 = 1 = your answer

Answer 39

the answer is 1

Answer 40

yes.

Answer 41

Which function grows at the fastest rate for increasing values of x?

h(x) = 5x^2 + x + 10

f(x) = 2 ⋅ 3^x

g(x) = 10x + 15

Answer 42

take a look at the exponents, which one do you think would result in the fastest growth?

Answer 43

C and A

Answer 44

there is only one correct answer

note - if you compare the exponents of h(x) and g(x) the exponent in h(x) is bigger than g(x) so it would grow faster

however, if you look at f(x), the exponent is x, which would cause it to grow much faster than an exponent of 2, since x will keep increasing in size

so f(x) grows the fastest

Answer 45

B

Answer 46

yes

Answer 47

https://static.k12.com/nextgen_media/assets/8090372-NG_AL1_O_04_U12_Quiz_01.png

The graph shows the quadratic function f(x) .


What is the average rate of change for the quadratic function from x = 10 to x = 12?

Enter your answer in the box.

________

Answer 48

same reasoning as before

f(12) - f(10) = ?

again, f(12) does not mean multiply f by 12, it means to find the value of the function at x = 12

Answer 49

2

Answer 50

not quite

f(12) = ? you must look at the graph to answer this

Answer 51

12

Answer 52

good

what about f(10) = ?

Answer 53

10

Answer 54

take a look at the graph

what is the value of the graph at x = 10?

Answer 55

14

Answer 56

what's the value of this point?

Answer 57

6

Answer 58

good, so f(12) - f(10) = 12 - 6 = 6

divide that by (12 - 10) to get 3 = your answer

Answer 59

3

Answer 60

the answer is 3

Answer 61

yes.