Question

Where are the asymptotes of f(x) = tan 4x from x = 0 to x = pi over two?

Answer 1

Asymptotes of a tan function are found form the formula
\[\theta=\frac{ n \pi }{ 2 }\]

Answer 2

theta=the value of b (in this case it's 4x)

Answer 3

What does the n stand for?

Answer 4

n=any odd integer...so once you solve for x...n can represent many numbers. (all asymptotes)

Answer 5

so it would be like \[4x = \frac{ 5\pi }{ 2 }\]

Answer 6

well 5pi could be one of the asymptotes.

but basically you want

\[x=\frac{ n \pi }{ 8 }\]

Answer 7

Where did the 8 come from?

Answer 8

you multiplied out the 4x to the denominator.

Answer 9

oh okay that makes more sense. But I am still confused of how to solve that equation to find the asymptotes

Answer 10

well, they give the domain from 0 to one period (pi/2)

start putting odd numbers in that equation to see if it fits the domain.

Answer 11

from what i can see, there are two asymptotes

Answer 12

at least from 0 to pi/2

Answer 13

any trouble?

Answer 14

Sorry my laptop is acting up, here are the answer choices:

x = pi over 4, x = 3 pi over 4
x = pi over 8, x = 3 pi over 8
x = 0, x = pi over 4
x = pi over 2, x = 3 pi over 2

Answer 15

yup it's in there alright

Answer 16

I am still confused on how to figure it out. I know to put in odd numbers, but should I put in the numbers from the answer choices?

Answer 17

Knowing that your domain is from 0 to pi/2

and that your asymptote finder equation is

\[\frac{ n \pi }{ 8 }\]
that basically means n can't be greater than 3

as pi/2=4pi/8

Answer 18

4 is a even number anyhow so it wouldn't work regardless

Answer 19

So, the answer would be C then?

Answer 20

no your equation was npi/8

the denominator must be 8

i'm pretty sure i just gave it away lol

Answer 21

Oh sorry I meant to say B. I'm not that good in math as you can tell

Answer 22

it's alright, you actually tried which is all that matters to me :)

Answer 23

anymore questions ?

Answer 24

Yeah, there is one section that I always get wrong:

Compare each of the functions shown below:


f(x)
graph of a downward facing parabola with vertex at 2, 3

g(x) = 2 cos(2x − π) + 2

h(x)
x y
−1 −7
0 −2
1 1
2 2
3 1
4 −2
5 −7

Which function has the largest maximum?

Answer 25

So...3 functions, and you want to know which the largest maximum value?

Answer 26

Yeah, I tried figuring it out but I don't know if it is right

Answer 27

Do you know if it's asking for the max x value...or max y value..?

Answer 28

It doesn't say if it is or not. But I assumed it meant maximum y value

Answer 29

Alright, then I think the max y value should be fairly clear in functions f(x) and h(x), can you tell me what they are ?

Answer 30

The maximum for f(x) is 3 and the maximum for h(x) would be 2

Answer 31

Now the slightly harder one..

do you know the max/min of g(x) = 2 cos(2x − π) + 2?

Answer 32

I have no idea

Answer 33

In the function g(x) = 2 cos(2x − π) + 2

there is a amplitude of 2, but also a vertical shift of +2

your max would be \[k+\left| a \right|\]
min would be \[k-\left| a \right|\]

Answer 34

k represents the vertical shift (+2)

a=amplitude

Answer 35

this is for the y value of course

Answer 36

So the maximum y value would be 4?

Answer 37

yep

Answer 38

Okay I get it now thank you!

Answer 39

yw. feel free to fan and medal, and tag me onto more questions :)