Question

https://static.k12.com/nextgen_media/assets/8078626-NG_AL1_J_06_U06_Quiz_03.png

The graph shows the function g(x) .

Select from the drop-down menu to correctly compare ​ g(x) ​ and f(x)=−3(x+1) .

The y-intercept of ​ f(x) ​ is _____________ the y-intercept of ​ g(x) ​ .

less than

greater than

equal to

Answer 1

@Vocaloid

Answer 2

I have answered this already, set x = 0 and calculate the y-intercept of f(x)

Answer 3

sorry i've been gone the time you've been answering me

Answer 4

and it's less than

Answer 5

good.

Answer 6

it's less than ?

Answer 7

yes.

Answer 8

could you help me if you're not busy ?

Answer 9

with more please with everything

Answer 10

sure

Answer 11

you're not busy with college or anything ?

Answer 12

today

Answer 13

I'm not busy right now

Answer 14

ok

Answer 15

The table shows the function ​ g(x) ​ .

Select from the drop-down menu to correctly compare the growth factors for the exponential functions g(x) and f(x)=4(3)x .


The growth factor of​ f(x) ​is __________________ the growth factor of g(x) .

less than

greater than

equal to

Answer 16

i'll send the pic

Answer 17

f(x) = 4(3)^x

Answer 18

if you look at the table of g(x) each value is being multiplied by 4 to get to the next value making 4 the growth factor of g

Answer 19

if you look at f(x) each number is being multiplied by 3 (the number with the exponent x) making 3 the growth factor of f

Answer 20

equal to

Answer 21

please review what I have said carefully

Answer 22

oh wait no

Answer 23

it's greater than

Answer 24

the growth factor of f(x) is 3
the growth factor of g(x) is 4

therefore the growth factor of f(x) is ______ than g(x)

fill in the blank

Answer 25

less than

Answer 26

good, that's it.

Answer 27

https://static.k12.com/nextgen_media/assets/8078601-NG_AL1_J_06_U06_Quiz_08.png

One day, Fiona and Heidi each bought coins at a coin shop. The equation f(x) = 3x + 12 represents the value of Fiona’s coin, in dollars, x years later. The graph shows the value of Heidi’s coin, in dollars, x years later.

Select from the drop-down menus to complete the statement.

When they bought their coins, ( Fiona's or Heidi's )

coin was worth ( $3, $6, $9, or $12 )

more than ( Fiona's or Heidi's ) coin.

Answer 28

hint: calculate f(x) at year 0 (when x = 0)

Answer 29

f(0) = 0

Answer 30

re-read the problem please

Answer 31

f(x) = 3x + 12

calculate f(x) when x = 0.

Answer 32

-4

Answer 33

replace "x" with "0" and calculate f(x).

Answer 34

f(0)

Answer 35

now calculate f(0).

Answer 36

f(0) = 0

Answer 37

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
f(x) = 3x + 12

calculate f(x) when x = 0.
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 38

copy down the original function

replace "x" with 0

then calculate what the function is equal to.

Answer 39

f(x)

f(0)

like this ?

Answer 40

write this down:

"f(x) = 3x + 12"

replace the "x" with "0" whenever x shows up

then calculate the function.

Answer 41

"f(x) = 3x + 12" = 12

Answer 42

good, f(0) = 12

Answer 43

now use the graph to find h(0).

Answer 44

so it's $12 right first ?

Answer 45

it is not $12

it is asking for the difference between heidi's coin and fiona's coin so we must subtract f(0) - h(0).

Answer 46

use the graph to find the value of heidi's coin at year 0

Answer 47

f(0) - h(0). = 0

Answer 48

again, use the graph to find the value of h(x) at x = 0.

Answer 49

ok i found it

Answer 50

what did you get as the value?

Answer 51

-10

Answer 52

correct me

Answer 53

-10 is not a value anywhere on the graph

Answer 54

put your finger on x = 0

then go up until you touch the graph

what value do you get for h(x)?

Answer 55

6

Answer 56

good, that's h(0)

Answer 57

so if f(0) = 12 and h(0) = 6

f(0) - h(0) = ?

Answer 58

f6

Answer 59

just 6 but good

Answer 60

6 right

Answer 61

so fiona's coin is worth more than heidi's coin by $6

Answer 62

Compounds A and B are used in an experiment.

The equation y = 500(0.5)^x represents the remaining amount of compound A, in grams, after x hours. The table shows the remaining amount of compound B.

What is the positive difference in the initial amount of each compound?

Enter your answer in the box.

__________ g

Answer 63

i'll send the pic

Answer 64

is it clear for you ?

Answer 65

so for compound A to find the initial amount just let x = 0 and find y

Answer 66

x = 0 = 0

Answer 67

y = 500(0.5)^x

what does y equal when x = 0 ?

Answer 68

all you have to do is replace "x" with "0" and calculate y

Answer 69

what i've been trying to tell you is 0

Answer 70

my computer was acting crazy

Answer 71

it is not equal to 0

Answer 72

y = 500(0.5)^0 = ?

Answer 73

y = 500

Answer 74

good, so that's the initial value of compound A

Answer 75

ok

Answer 76

so for compound B we need to determine what the mass is at h = 0

Answer 77

since it's decreasing by half each hour, we have to double the mass at h = 1 to get the mass at h = 0 (since we are going backwards in time)

Answer 78

so the initial mass of B is 400 making the difference 500 - 400 = 100 = your answer.

Answer 79

so it's 400 g

Answer 80

or 100 g ?

Answer 81

100

Answer 82

ok 100 g ?

Answer 83

The linear function f(x) passes through the points (0,1) and (2,7).

A few values from the exponential function g(x) are shown in the table.

What is the positive difference in the y-intercept value of ​ f(x) ​and g(x) ​?

Enter your answer in the box.

_____

Answer 84

i'll the send pic

Answer 85

to find g(1) and g(0) we have to think in reverse

since the value of g(x) is being doubled for every increase in x, we have to divide by 2 to get g(1) and g(0)

Answer 86

g(1) is (1/2) of g(2) and g(0) is (1/2) of g(1)

Answer 87

so if g(2) is 12 what is g(1)?

Answer 88

(1/2)

Answer 89

g(1) is ~one half~ the value of g(2)

so if the value of g(2) is 12, what is the value of g(1)?

Answer 90

g(0)

Answer 91

to find g(1), take the value of g(2) and divide by 2

Answer 92

so if the value of g(2) is 12, what is the value of g(1)?

Answer 93

12/g

Answer 94

divide by 2, not divide by g.

Answer 95

6

Answer 96

good, now to find g(0) divide the value of g(1) by 2

Answer 97

3

Answer 98

good so the intercept of g(x) is 3 and the intercept of f(x) is 1 making the difference 2 = your answer

Answer 99

it's 2 ?

Answer 100

yes

Answer 101

ok

Answer 102

Which ordered pairs lie on the graph of the exponential function f(x)=128(0.5)^x ​ ?

Select each correct answer.

(0, 1) ​

​ (1, 64) ​

​ (3, 16) ​

​​ (8, 0.5) ​

Answer 103

you just have to test each x value to see if it produces the matching y value

Answer 104

for example, for (0,1) let x = 0 and see if f(x) = 1

Answer 105

right

Answer 106

good, (0,1) works, now repeat these steps for the other points

Answer 107

(1,64) wrong​

​ (3,16) ​correct

​​ (8,0.5) ​correct

Answer 108

128(0.5)^1 = ?

Answer 109

64

Answer 110

good, so (1,64) works

all of the points work, actually

Answer 111

all of them ?

Answer 112

yes

Answer 113

https://static.k12.com/nextgen_media/assets/8078551-NG_AL1_SemA_06_UT_40.png

Which function represents the graph of y=4^x−1 ?


A. q

B. r

C. s

D. t

Answer 114

btw the answer is C

Answer 115

is the -1 within the exponent or not?

Answer 116

yes

Answer 117

but i graphed it so it shows it's correct

Answer 118

as a hint try plugging in x = 0 and you'll get y = (1/4) making s not an option

Answer 119

there's only one graph that crosses (0,1/4)

Answer 120

i plugged it in so now i see it like this

the choices: q, r, s, or t

so it's not q s or r

Answer 121

you have to be careful with parentheses

Answer 122

y = 4^(x-1) try graphing this

Answer 123

oh ok now i get it

Answer 124

it's r

Answer 125

r is correct

Answer 126

https://static.k12.com/nextgen_media/assets/8079952-NG_AL1_SemA_06_UT_15.png

The function f (x) = 5^(x−1) is shown on the coordinate plane.

Select from the drop-down menus to correctly describe the end behavior of ​ f(x) ​.

As x decreases without bound, the graph of f(x)

Choose: approaches y = 0, increases without bound, or decreases without bound

As x increases without bound, the graph of f(x)

Choose: approaches y = 0, increases without bound, or decreases without bound

Answer 127

as x goes to -infinity, the graph approaches y = 0

but what about x going to + infinity? what happens as x gets bigger and bigger?

Answer 128

it increases

Answer 129

good so y "increases without bound"

Answer 130

so the first answer is "approaches y = 0"
second is "increases without bound"

Answer 131

Let f(x)=8^x and g(x) = 8^x+5 + 1 .

Which transformations are needed to transform the graph of f (x) to the graph of g (x) ?

Select each correct answer.

horizontal translation 5 units left

vertical translation 5 units up

horizontal translation 1 unit left

horizontal translation 5 units right

vertical translation 1 unit down

vertical translation 1 unit up

Answer 132

guide for function transformations: http://www.onlinemathlearning.com/image-files/xrules-transformation-function.png.pagespeed.ic.D7TvNh8Eh1.png

Answer 133

anyway, since we add + 1 to the entire function it goes up 1 unit

Answer 134

the first one

the third one

the 5th one

the 6th one

Answer 135

and since we add 5 to x (not from the entire function) it goes to the left by 5

Answer 136

the first one

the third one

the 5th one

the 6th one

100% correct for sure

Answer 137

correct me

Answer 138

there are only two correct answers, a vertical transformation up by 1 and horizontal left by 5

Answer 139

the 6th one and the first one ?

Answer 140

right

can we open a new question, this one is getting kind of laggy

Answer 141

ok sure