Question

Identify the discontinuities, graph, and find the zeros of f(x) = 4x^2 - 36x / x - 9?

Answer 1

Can someone help??

Answer 2

evidently it will not be continuous at \(x=9\) because you cannot divide by zero

Answer 3

To find the 0's of the function set f(x) = 0 and solve for x

Answer 4

\[\frac{4x^2-36x}{x-9}=\frac{4x(x-9)}{x-9}=4x\] if \(x\neq 9\)

Answer 5

Ok so discounity is 9

Answer 6

yes

Answer 7

and it will be 0 if \(x=0\)

Answer 8

I got the 4x but what would that be for?

Answer 9

the function is really just \(f(x)=4x\) which is a line with slope 4 through the origin
but it is undefined if \(x=9\)

Answer 10

Ok so discontinuities is 9 and the zeros you find by putting f(0) and solving it like that?

Answer 11

evidently \(4x=0\) if \(x=0\) so the answer to "find the zeros" is \(x=0\)

Answer 12

you do not find the zeros by finding \(f(0)\) but rather by setting \(f(x)=0\) and solving for \(x\)
it just so happens that in this case \(x=0\) is also the answer

Answer 13

I still a little stuck

Answer 14

ok lets answer the questions one by one

Answer 15

Ok thanks :)!

Answer 16

Identify the discontinuities
answer: it is discontinuous at \(x=9\) because you cannot divide by 0

Answer 17

That part I got :)

Answer 18

The rest just confuses me :(

Answer 19

graph
answer: the graph is identical to the graph of the line \(y=4x\)
a line with slope \(4\) through the origin
the only difference is that at \((9,36)\) since the original function is not defined at \(x=9\) you have a hole

Answer 20

So you times 4 by the 9 and got 36 for y, right?

Answer 21

yes, exactly

Answer 22

So I so far get 9 is the discounity and by zeros are (9,36) is that correct?

Answer 23

find the zeros
answer : if \(x=0\) then \(f(x)=0\)

Answer 24

no, the discontinuity is at \((9,36)\) the zero is at \(x=0\) because that is where the line crosses the \(x\) axis

Answer 25

they are two separate concepts

Answer 26

So wherever the line crosses the x axis is the zero?

Answer 27

yes
it is also the solution or the solutions to \(f(x)=0\)

Answer 28

So I have to graph to find the zero?

Answer 29

no not really
you can set \(4x=0\) and solve for \(x\) (in your head)

Answer 30

Ohh I see what you did

Answer 31

So the zero=0

Answer 32

and discounity is (9, 36)

Answer 33

yes
or you could just say the discontinuity is at \(x=9\)
either way

Answer 34

Am I missing anything else?

Answer 35

no i don't think so

Answer 36

Thanks! for your help! :) :)

Answer 37

yw