Question

Let f(x) = 6(2)^x−1 + 4 .

The graph of f(x) is stretched vertically by a factor of 4 to form the graph of g(x) .

What is the equation of g(x) ?

Enter your answer in the box.

g(x) = ___________

Answer 1

I am not 100% sure on this but I believe you would just multiply this part 6(2)^(x−1) by 4 to get 24(2)^(x-1) and leave everything else alone :S

Answer 2

6(2)^(x−1) x 4 ?

Answer 3

yes

Answer 4

@sillybilly123 can you double check this I am having a brain fart on this question ;_;

Answer 5

let me the pic

Answer 6

24(2)^(x-1) + 4 is my best guess

Answer 7

the answer ?

Answer 8

yes

Answer 9

The graph of g(x) is a transformation of the graph of f(x) = 3^x .

https://static.k12.com/nextgen_media/assets/8122706-AL1_UT_A6_Pool6_NP100_267.png

Enter the equation for g(x) in the box.

g(x) = ___________

Answer 10

seems like it's up 1 unit and to the left 2 units

Answer 11

so you would add 1 to the entire function, and then add 2 to exponential part

Answer 12

1 + 2

Answer 13

i know it's not correct

Answer 14

so adding 1 to the entire function would just be sticking a +1 at the end to get

f(x) = 3^x + 1

adding 2 to the exponential part would just be adding 2 to x only

so f(x) = 3^(x+2) + 1 would be my best guess as the final answer

Answer 15

g(x) = f(x) = 3^(x+2) + 1

Answer 16

it's not equal to f(x) but otherwise yeah

g(x) = 3^(x+2) + 1

Answer 17

g(x) = 3^(x+2) + 1 this one ?

Answer 18

yes

Answer 19

The graph shows the parent function f(x)=2(0.5)^x.

https://static.k12.com/nextgen_media/assets/8079954-NG_AL1_SemA_06_UT_29.png

Which graph represents the function g(x) = 2(0.5)^x − 1?

A. https://static.k12.com/nextgen_media/assets/8079958-NG_AL1_SemA_06_UT_33.png


B. https://static.k12.com/nextgen_media/assets/8079956-NG_AL1_SemA_06_UT_31.png

C. https://static.k12.com/nextgen_media/assets/8079955-NG_AL1_SemA_06_UT_30.png

D. https://static.k12.com/nextgen_media/assets/8079957-NG_AL1_SemA_06_UT_32.png

Answer 20

depends on whether the -1 is part of the exponent or not

Answer 21

if it's part of the exponent it's a transformation 1 to the right

if it's not part of the exponent it's a transformation 1 down

Answer 22

\[ 2(0.5)^{x − 1}\] this?

Answer 23

yes

Answer 24

then it's to the right 1 unit

Answer 25

wait no

Answer 26

x up and - 1 down

Answer 27

well, we can eliminate 2 choices based on the shape of the graph alone

Answer 28

b and a

Answer 29

so A and D are the wrong shape so we can eliminate these

Answer 30

which graph is the original graph translated 1 unit down? b or c?

Answer 31

c

Answer 32

awesome good work ^_^

Answer 33

https://static.k12.com/nextgen_media/assets/8079943-NG_AL1_SemA_06_UT_34.png

The linear function in the graph shows the value, in dollars, of an investment in years after 2012.

The exponential function in the table represents the balance of a savings account, in dollars, over time in years after 2012.

How does the y-intercept of the exponential function compare to the y-intercept of the linear function?

Drag the correct answer to the box to complete the statement.


approximately 130 more than
approximately 130 less than
approximately 30 more than
approximately 30 less than


The y-intercept of the exponential function is ____________ the y-intercept of the linear function.

Answer 34

i'll send pic

Answer 35

so each consecutive year the balance is being multiplied by 3

to go backwards we do the opposite, by dividing by 3

Answer 36

if the year 2 value is 180, we can get the year 1 value by dividing the year 2 balance by 3

Answer 37

so 180/3 = ?

Answer 38

60

Answer 39

good, and to get the year 0 we divide that by 3

so 60/3 = ?

Answer 40

20

Answer 41

good so the exponential y-intercept is 20

what about the y-intercept of the graph?

Answer 42

the y - intercept is 30 less

Answer 43

just look at the graph for now (not the exponential part/calculations.etc)

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

Answer 44

the answer for this is 0

Answer 45

my computer was acting up again

Answer 46

put your finger on the graph when x = 0

then go up until you touch the graph

Answer 47

10

Answer 48

what is the value of the graph at this point?

Answer 49

150

Answer 50

good, 150

Answer 51

so the difference between the linear and exponential y-intercepts is: 150 - 20 = 130

Answer 52

so therefore is 130 more or less so it's more

Answer 53

and since we've solved it it's more

Answer 54

we need to pay attention to how the question is phrased

Answer 55

The y-intercept of the exponential function is ____________ the y-intercept of the linear function.

since the exponential y-intercept was less than the linear intercept, "less than" needs to be in the blank

Answer 56

oh i had that first but ok

Answer 57

What is the average rate of change of the function on the interval from x = 1 to x = 2?

f(x) = 10(5.5)^x



Enter your answer, as a decimal, in the box.

___________

Answer 58

average rate of change formula

Answer 59

"5.5" was replaced by "(55/10)".

Answer 60

start by calculating f(2) and f(1)

using f(x) = 10(5.5)^x

Answer 61

f(2) - f(1) right ?

Answer 62

yes, but you must calculate f(2) and f(1) separately using the equation, then subtract the results

Answer 63

f(2) means let x = 2 and calculate f(x)

Answer 64

f(2)=(4)^x-1 right ?

Answer 65

or no

Answer 66

wait

Answer 67

my apology

Answer 68

generally you do not carry over information from other problems into new problems

Answer 69

in this problem, f(x) = 10(5.5)^x

Answer 70

f(2) = 10(5. 5)^x

Answer 71

right ?

Answer 72

you're on the right track, but you also need to replace the other x with 2

Answer 73

f(2) = 10(5. 5)^2 = ?

Answer 74

f = 605/4 = 151.250

Answer 75

remember that the 2 exponent only gets applied to the 5.5

Answer 76

calculate 5.5^2 and then multiply the result by 10

Answer 77

112
——— = 30.25000 the answer for 5. 5^2
22

Answer 78

you can just use a calculator for these ^_^

Answer 79

121x^10
——————
4

Answer 80

is it correct ?

Answer 81

you can just type calc into google to give you a calculator

Answer 82

ok type what into the calculator again ?

Answer 83

10(5. 5)^2 =
this

Answer 84

302.5

Answer 85

good now do the same thing with 10(5. 5)^1

Answer 86

55

Answer 87

good now those are our f(2) and f(1) values

now we plug these into the average rate of change eqn

Answer 88

[f(2) - f(1)]/(2-1) = (302.5 - 55)/(2-1) = ?

Answer 89

247.5

Answer 90

good that's our answer ^^

got to go now, have a great night ~

Answer 91

wait wait