Question

The graph below shows three functions:


Which function has all real numbers as its domain?

Only f(x)
Both g(x) and p(x)
Both f(x) and g(x)
Only p(x)

pease explain so i will understand

Answer 1

the domain of a function is the the section of the x axis for which the function exists. To say that the domain has all real numbers means the entire x axis (from minus inf to plus inf) has some corresponding function value (no gaps, no hard stops, etc.). Based on this can you tell which function of the three satisfies that?

Answer 2

p(x) and g(x)?

Answer 3

pick an example, say, x=4. p(x) is not defined for that x (its domain "ends" somewhere around 1). Same for g(x). So p(x) and g(x) both can be safely excluded from the answer .

Answer 4

ooh okay Thank you so it would be A?

Answer 5

could you help me understand like two more?

Answer 6

I agree - only f(x) seems to have the domain stretch from -inf to +inf, i.e., all real numbers

Answer 7

you mean two other problems?

Answer 8

yeah

Answer 9

sure - are they related to the same graph?

Answer 10

no

Answer 11

The average annual salary of the employees of a company in the year 2005 was $70,000. It increased by the same factor each year and in 2006, the average annual salary was $82,000. Let f(x) represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and f(x)?

f(x) = 70(1.17)^x
f(x) = 82(1.17)^x
f(x) = 70(2.2)^x
f(x) = 82(2.2)^x

Answer 12

this would be c or d right?

Answer 13

Hmm, so I think c and d you can safely eliminate by simply plugging in x=1 and checking the value f(1)

Answer 14

(c): 70*2.2^1=154 (thousand $)

Answer 15

(d) similarly, too high

Answer 16

what you want to get is something close to 82 (thousand)

Answer 17

try (a) what do you get?

Answer 18

81.9

Answer 19

70*1.17=81.9?

Answer 20

yes, so that's pretty close. (b) is too high. So it looks like that (a) "best represents" the relationship

Answer 21

Thank you

Answer 22

last one








A store had 150 laptops in the month of January. Every month, 20% of the laptops were sold and 10 new laptops were stocked in the store.

Which recursive function best represents the number of laptops in the store f(n) after n months?

f(n) = 150 − 0.8 × f(n − 1) + 10, f(0) = 150, n > 0
f(n) = 0.2 × f(n − 1) + 10, f(0) = 150, n > 0
f(n) = 0.8 × f(n − 1) + 10, f(0) = 150, n > 0
f(n) = 150 + 0.8 × f(n − 1) + 10, f(0) = 150, n > 0

Answer 23

would you like to make a guess?

Answer 24

I would go with C

Answer 25

me too i think you're correct! do you know why?

Answer 26

no not really

Answer 27

okay, so the function is recursive, meaning it takes the previous value of itself, does something to it, and outputs a new value. Now, the reason for c being correct is the following

Answer 28

the term 0.8 x f(n-1) covers the part that says they sell 20% of their stock every month - in other words 80% of the previous month remains (0.8)

Answer 29

the other term +10 covers the fact that they get 10 new laptops added to their stock

Answer 30

and there is no other non-sense term, like with a or d (the +150)

Answer 31

is it a little clearer?

Answer 32

Yes!!

Answer 33

Thank youuu

Answer 34

Cool! No problem