Question

The function f(x) is shown below.

f(x) = (2)x+1

The function f(x) is shifted to the left by 13 units. Which of the following best represents the new function?

f(x) = (2)x + 13

f(x) = (2)x + 14

f(x) = (2)x -12

f(x) = (2)x - 13

Answer 1

hint: to shift f(x) to the left by 13 units, you have to replace x with x-13. So you need to evaluate f(x-13)

Answer 2

thank you!! :) I hav another question if u could help me with

Answer 3

Wendy enjoys listening to hip hop and downloads music regularly from the internet. She already has four hours of hip hop in her collection. From the second month onward, the number of hours of hip hop music she downloads each month is nine percent greater than the number of hours of hip hop music she had downloaded the previous month. Which function best shows the total number of hours of hip hop music Wendy has in her collection f(x) after x months?

f(x) = (1.09)x + 3

f(x) = 3(1.09)x

f(x) = (1.09)x + 2

f(x) = (1.09)x - 2

Answer 4

Odd...it mentions '4' but I don't see it anywhere in any of the functions.

Answer 5

You sure it's not "3 hours" instead of "4 hours"?

Answer 6

idk it says four

Answer 7

can u help me with this one instead
Which exponential function goes through the points (1, 8) and (4, 64)?

f(x) = 4(2)x

f(x) = 2(4)x

f(x) = 4(2)-x

f(x) = 2(4)-x

Answer 8

plug x = 1 into each function and evaluate

if you get y = 8, then you're on the right track

if you don't get y = 8, then you can eliminate that answer choice

Answer 9

same thing for x = 4

you should get y = 64

if you don't, then eliminate that choice

Answer 10

is it f(x) = 2(4)x

Answer 11

what happens when x = 4?

Answer 12

it not that one because it becomes 32 right

Answer 13

the function is f(x) = 2(4)^x

Answer 14

not f(x) = 2(4)x

Answer 15

i don't understand this

Answer 16

f(x) = 2(4)^x

f(4) = 2(4)^4

f(4) = ???

Answer 17

2*4=8 so 8*8*8*8?

Answer 18

what is 4^4?

Answer 19

256

Answer 20

now multiply that by 2

Answer 21

512

Answer 22

so f(4) = 512, but we wanted f(4) to be equal to 64

Answer 23

so what do we need to do now

Answer 24

so clearly (4,64) is NOT on the graph of f(x) = 2(4)^x

Answer 25

so it's the first one because f(4) = 4(2)4= 4*4=16 16*4=64 and f(1) = 4(2)1=1*2=2 and 2*4=8

Answer 26

it's a bit hard to follow your steps, but yeah it's the first one

Answer 27

Thank you so much i just have one more question
The table below shows the values of f(n) for different values of n.


n 1 2 3 4 5 6
f(n) 1 2 2 4 8 32


Which recursive function best represents the values shown in the table?
f(1) = 1, f(2) = 2, f(n) = f(n -1) f(n - 2); n > 2

f(1) = 1, f(2) = 2, f(n) = f(n -1) + f(n - 2); n > 2

f(1) = 1, f(2) = 2, f(n) = f(n -3) + f(n - 2); n > 2

f(1) = 1, f(2) = 2, f(n) = f(n -3) f(n - 2); n > 2

Answer 28

do you know how recursive functions work?

Answer 29

not that well

Answer 30

what is f(3) in this case (look at the table)

Answer 31

idk

Answer 32

look for n = 3, then look below that

Answer 33

the 2

Answer 34

so f(3) = 2

Answer 35

so let's say the function was f(n) = f(n -1) + f(n - 2)

if that were true, then plugging in n = 3 gives us

f(n) = f(n -1) + f(n - 2)

f(3) = f(3 -1) + f(3 - 2) ... plug in n = 3 (ie replace each n with 3)

f(3) = f(2) + f(1)

what's the next step?

Answer 36

u add f(2) and f(1)

Answer 37

what is f(2) and f(1)?

Answer 38

they are given in the table

Answer 39

1 and 2

Answer 40

idk this stuff

Answer 41

that means

f(3) = f(2) + f(1)

becomes

f(3) = 2+1

f(3) = 3

but remember we wanted f(3) to be equal to 2 (and not 3)

Answer 42

so it needs to be subtraction

Answer 43

so that means that f(n) = f(n -1) + f(n - 2) cannot be the answer

why not? because when you plug in n = 3 you get f(3) = 3 when you should get f(3) = 2

Answer 44

see how I eliminated that answer choice?

Answer 45

ya

Answer 46

f(x)=2x - 12
because you shift to the left 13=> 1-13=-12

Answer 47

What's the answer?