Question

help with calculus!

Answer 1

State the vertical, horizontal asymptotes and zeros of the rational function, f(x) =

Answer 2

Why is there no zero at x = –1?

Answer 3

@jim_thompson5910

Answer 4

x = negative1

Answer 5

factor the numerator to get ???

Answer 6

(x+2)(x+1)

Answer 7

and the denominator?

Answer 8

(x+4)(x+1)

Answer 9

what terms cancel?

Answer 10

(x+1)

Answer 11

we're left with (x+2)/(x+4)

Answer 12

yeahh

Answer 13

that's why there isn't a zero at x = -1

Answer 14

also, x = -1 is not in the domain (because it causes a division by zero error)

Answer 15

gotchaa

Answer 16

how do i get the certical , horizontal ,and zero?

Answer 17

set the denominator equal to zero and solve for x to get the vertical asymptote

focus on the simplified expression

Answer 18

is the vertical asymptotes -4 and -1?

Answer 19

focus on the simplified expression

Answer 20

what does that mean

Answer 21

i dont understand

Answer 22

when you cancelled out x+1

Answer 23

you are left with (x+2)/(x+4)

Answer 24

focus on (x+2)/(x+4)

Answer 25

oh so just -4

Answer 26

the vertical is -4 right?

Answer 27

yes

Answer 28

and how do i do horizontal?

Answer 29

The leading terms are x for each numerator/denominator

Divide the leading terms: x/x = 1

So the horizontal asymptote is y = 1

Answer 30

got it!

Answer 31

and how do i get the zeros??

Answer 32

this works because the degrees for numerator & denominator are the same

Answer 33

set the numerator equal to zero to get the zeros

focus on (x+2)/(x+4)

Answer 34

so the zeros are -2 and -4, right?

Answer 35

the numerator

Answer 36

oh so just -2

Answer 37

yes

Answer 38

the denominator can't be 0

so only the numerator can

Answer 39

thanks!

Answer 40

np