Question

what is the asymptote of 4/x-5

Answer 1

@Astrophysics

Answer 2

@chainedecho

Answer 3

@adi3

Answer 4

@milk333

Answer 5

@color he is offline

Answer 6

@Awolflover1 @chalkskull

Answer 7

@iGreen @igigighjkl

Answer 8

Hu?

Answer 9

Horizontal or vertical asympotote?

Answer 10

asymptote*

Answer 11

both

Answer 12

If vertical, solve the equation in the denominator.

x - 5 = 0

Can you solve that for 'x'?

Answer 13

I in 6th grade...

Answer 14

me don't no.

Answer 15

x = 5

Answer 16

Correct, that's our vertical asymptote.

Answer 17

ok

Answer 18

To find horizontal asymptotes:
If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

Answer 19

What's the degree of the numerator?

Answer 20

how do you check that

Answer 21

Degree is the highest exponent.

4 is the only term in the numerator, do you know what the degree is?

Answer 22

The degree of every regular number is 1.

Because \(\sf 4^1 = 4\)

Answer 23

So the degree of the numerator is 1.

How about the denominator?

Answer 24

but we got taught like this. we need to make both zero

Answer 25

Oh wait..the degree is actually 0..nevermind.

Answer 26

Since there is no variable in the numerator it's 0..for the denominator, we have an 'x', so what's the degree there?

Answer 27

1

Answer 28

Correct..so the degree in the numerator is less than the degree in the denominator..so look back at the statements I posted earlier and tell me what the horizontal asymptote will be.

Answer 29

horizontal is 5 vertical is 0

Answer 30

but isnt 4^0 1 too

Answer 31

That has nothing to do with this.

Answer 32

We said the degree in the numerator is less than the degree in the denominator..so which statement matches that?

If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).

If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

Answer 33

a

Answer 34

Yep! So the horizontal asymptote is the x-axis or y = 0

Answer 35

VA is x = 5
HA is y = 0