Question

i love ham

Answer 1

@amymsmith2121 I'll help you but it'd be an interactive session. Would you respond to my simple questions???

Answer 2

ok

Answer 3

We have
\[f(x)=\frac{(x+a)(x+b)}{(x+c)(x+d)}\]
You know what is a zero, asymptote and hole???

Answer 4

yes, I do

Answer 5

Tell me???

Answer 6

a hole is a missing part of the graph's points. An asymptote is a line that a graph approaches, but does not intersect

Answer 7

A zero???

Answer 8

Where a function equals the value zero (0).

Answer 9

Great:)
So tell me the zeros of this function???

Answer 10

I don't know how I could know that if I only have variables...

Answer 11

We have
\[f(x)=\frac{(x+a)(x+b)}{(x+c)(x+d)}\]
Put x=-a , see what will you get?

Answer 12

x=-a will make the numerator zero, so f(-a)=0

Answer 13

oohh k

Answer 14

so tell me the other zero
??

Answer 15

b?

Answer 16

correct, can you tell me the asymptote for this???

Answer 17

put x=-c , what's f(-c)??

Answer 18

d?

Answer 19

if x=-c, then denominator becomes 0, which makes
f(-c)= finite/zero
which is infinity
so -c is an asymptote

Answer 20

can you tell e the other asymptote???

Answer 21

-a

Answer 22

*me

Answer 23

X=-a will make numerator zero, what will make the denominator zero?

Answer 24

@amymsmith2121 ????

Answer 25

i don't know. i'm sorry

Answer 26

In the denominator, we have
(x+c)(x+d)
so when x=-c or x=-d then it'll be zero which will make function f go toward positive or negative infinity, so x=-c and x=-d are the asymptotes of function

Answer 27

ok, i think i understand

Answer 28

Great, did you understand how to find zeros?

Answer 29

when x=-c or x=-d

Answer 30

Zeros of function, when f(x)=0

Answer 31

can you show me an example with real numbers? variables are confusing

Answer 32

Okay.
say we have
\[f(x)=\frac{(x+2)(x-3)}{(x+4)(x-5)}\]
When x=-2
\[f(-2)=\frac{(-2+2)(-2-3)}{(-2+4)(-2-5)}=\frac{0 \times (-2-3)}{(-2+4)(-2-5)}=\frac{0 \times -5}{2 \times -7}=0\]
so x=-2 is a zero , if you put x=3 then also f will be zero!!!!
so x=-2 and x=-3 are the zeros

Answer 33

Did you understand this?

Answer 34

Gross