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Mathematics 64 Online
kaylak:

help

Pennywise:

Okay?

kaylak:

@Vocaloid

kaylak:

give me a sec

kaylak:

@Vocaloid

kaylak:

@Vocaloid

kaylak:

i know it is an exponential function but not sure why

Vocaloid:

we can re-write it so it looks like y = ab^x

Vocaloid:

f(x) = 3^(2x-3) if we apply our exponent rules we can get f(x) = 3^(2x)/3^3

kaylak:

so b?

Vocaloid:

hold on let me check something

Vocaloid:

having a bit of a brain fart, trying to re-write 3^(2x) in terms of 3^x but don't remember how

Vocaloid:

(other than (3^x)^2)

Vocaloid:

ok apparently it's base 9 (D) had to use software for this >>

kaylak:

oh ok working on 2 to see if i can figure it out

Vocaloid:

for x ----> - infinity, what happens to the value of b^x?

kaylak:

it's a or c

Vocaloid:

hint: b^x goes to 0 for very large negative x

Vocaloid:

but what about very large positive x?

kaylak:

i didn't get an exonential function i got some shaded crap

Vocaloid:

you don't have to rely on a graph for this, you can think about it in terms of algebra what is the value of b^x like if x is something very large like 1000000?

kaylak:

so it is c because when f is infinity x is too

kaylak:

right?

Vocaloid:

not quite see how it says "as x ---> 0"? that's not end behavior

Vocaloid:

end behavior is x---> + infinity or x ---> - infinity

Vocaloid:

try to think about some of the clues I have given you

kaylak:

the graph has the line at the one because when you do an exponent to the first power it's itself and 0 is 1

Vocaloid:

again, try not to rely on the graph, you don't always have the option of graphing

kaylak:

so 0 makes sense

Vocaloid:

we are asking about "end behavior" which is the behavior of the graph when x ---> positive or negative infinity it does not make any sense to look at the function when x ---> 0 because that's not end behavior

Vocaloid:

x = 0 is the middle of the graph not the end

Vocaloid:

here are the clues I have given you: when x is a very large negative number, the function goes to 0 when x is a very large positive number, the function goes to very large positive numbers use these clues to find the best answer

Vocaloid:

what did you get for #2?

kaylak:

a?

kaylak:

0 to -infinity

Vocaloid:

good! A

kaylak:

i knew it was a or c

Vocaloid:

4 looks good to me

kaylak:

3 more questions

Vocaloid:

hint: can y = ab^x be negative if a and b are positive?

kaylak:

no unless you have it is a negative exponent like to the 3 or something

Vocaloid:

even with a negative exponent, it's still positive! for example, (2)(3)^(-3) is still positive

Vocaloid:

so your domain is all reals and your range is all real positives

kaylak:

so what would the answer be?

Vocaloid:

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid so your domain is all reals and your range is all real positives \(\color{#0cbb34}{\text{End of Quote}}\) ^ use this information to find the answer

kaylak:

is it a because b is less than 1 but a real number so -infinity ,0

kaylak:

@Vocaloid

Vocaloid:

hint: how do you express "all positive numbers" in interval notation?

kaylak:

]

Vocaloid:

try one more time. "the positive numbers range from ____ to _____" try filling in the blanks

kaylak:

only have like 10 min left

kaylak:

then i have to go

kaylak:

infinity to inifinity

kaylak:

and the negative is the same for negative but that's not an answer choice

kaylak:

so we are down to c or d then

Vocaloid:

hint: positive numbers start at 0 (not including 0)

Vocaloid:

so "all positive numbers" becomes (0,infinity) in interval notation

Vocaloid:

how can we express "all real numbers" in interval notation?

kaylak:

(-infinity,infinity) ?

kaylak:

so c?

Vocaloid:

awesome, so c is the ans.. for #2

kaylak:

can you check my other 2 then 1 more

Vocaloid:

3 is right

Vocaloid:

for 4, x = 1, f(x) = e how can we express this as a point (x,y)?

kaylak:

1,e

Vocaloid:

good, so C not D

Vocaloid:

last one? I gotta work on my own hw soon ^_^"

kaylak:

this is it

kaylak:

i'm virtual school lol don't have hw just a lot of assignments

Vocaloid:

for #1 you would also include f(x) = (-5)^x

Vocaloid:

so 1,2,4

kaylak:

only 2 answers though and i graphed the secod one and it didn't turn out one

kaylak:

2 points mean 2 answers

Vocaloid:

oh that's odd :S maybe just go with 1 and 4 then

kaylak:

ok lol i tried clicking 3 answers didn't work said only 2 answers

kaylak:

yep it's 1 and 4

kaylak:

thank you bye

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