Question

The functions f(x) and g(x) are described using the following equation and table:

f(x) = 3(1.02)^x


x g(x)
-1 -4
0 6
1 8
2 10


Which statement best compares the y-intercepts of f(x) and g(x)?
The y-intercept of f(x) is equal to the y-intercept of g(x).

The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).

The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

Answer 1

The y-intercept is where x=0, so solve for x=0 in f(x)
\(f(x) = 3(1.02)^0=3(1)=3\)

for g(x), they give you a table and directly tell you that for x=0, g(x) 6 so the intercept for g(x) is 6

Answer 2

@kirbykirby : so which awnser is it?

The y-intercept of f(x) is equal to the y-intercept of g(x).

The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).

The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

Answer 3

for f(x) it's 3
for g(x) it's 6

how to you get from 3 to 6 according to the choices given?

Answer 4

c? @kirbykirby

Answer 5

yes indeed :)!

Answer 6

Yay! do you mind helping me some other questions?

Answer 7

ok sure

Answer 8

@kirbykirby

Answer 9

The graph of f(x) =(0.5)^x is replaced by the graph of g(x) =(0.5)^x-k. If g(x) is obtained by shifting f(x) down by 5 units, the value of k is _________.

Answer 10

@kirbykirby

Answer 11

5, since there is already a negative in front of k

Answer 12

thank you!

Answer 13

@kirbykirby

Answer 14

Which function do you think could represent f(x), and which one do you think represents g(x) ?

Answer 15

B?

Answer 16

not quite

Answer 17

if \(f(x)=4^x\) and \(g(x)=-1\)
then \(f(x) + g(x) = 4^x + (-1)\)

Answer 18

oh so D

Answer 19

yup

Answer 20

Sorry this is part of my finals @kirbykirby

Answer 21

would you mind helping me with the questions?

Answer 22

are there a lot more

Answer 23

@kirbykirby

Answer 24

5 more

Answer 25

actually help me with these two and ill be gone lol @kirbykirby :)

Answer 26

11, does it look exponential or linear?

Answer 27

linear

Answer 28

if it's linear, then the amount of increase will be the same for x=1, x=2, x=3...
So like if
x=1 with value 50
x=2 with value 60
x=3 with value 70

this is a linear increase since it's always increasing by the same amount 10.

Answer 29

if you subtract the values from x=3 and x=2, and compare it to the subtraction of x=2 and x=1 and see that its not the same, it will be exponential, if it's the same then it's linear

Answer 30

C!

Answer 31

it would actually be D. The equal increase by a factor would imply a multiplication, whereas an increase in number would mean a simple increase as I mentioned above (+10, +10...)

The function represented would actually be \(\large 50(5)^{x-1}\), so it's constantly increasing by a factor of 5 (meaning you constantly multiply that number by 5
50 -> 250, multiply by 5
250 -> 1250 , multiply by 5

Answer 32

Ohhhhhhhhh ok i got it :) thanks and what about 12?

Answer 33

Try to determine which options are increasing by adding a number every time, or by multiplying a number every time

If you are adding : it's linear
If you are multiplying: it's exponential

Answer 34

so C?

Answer 35

in option one, you keep doing +0.3, +0.3.. so it can't be exponential

Answer 36

Ohhh okay :) thank you very much!

Answer 37

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