Question

What is the discontinuity and zero of the function f(x) = the quantity of 3 x squared plus x minus 4, all over x minus 1?

Answer 1

Discontinuity at (-1, 1), zero at (four thirds, 0)

Discontinuity at (-1, 1), zero at (negative four thirds , 0)

Discontinuity at (1, 7), zero at (four thirds , 0)

Discontinuity at (1, 7), zero at (negtive four thirds, 0)

Answer 2

@ganeshie8

Answer 3

\[f(x)=\frac{3x^2+x-4}{x-1}\]

Answer 4

Yes that's what it looks like.

Answer 5

To find when f=0 find when top=0
To find when f is discontinuous from when bottom=0

Answer 6

What?

Answer 7

To find f=0 is to find the zeros.
To find the zeros, find when top=0.

Answer 8

The top is 3x^2+x-4

Answer 9

So set it equal to zero?

Answer 10

top=0 yes

Answer 11

and then you need to also find when bottom=0

Answer 12

3x^2+x-4=0
and
x-1=0

Answer 13

3x^2+x-4=0 will give you the zeros of f (aka when f=0)

x-1=0 will give you the discontinuities

Be careful though. If you get a zero of the top that is also a discontinuity of the bottom, then as of whole it is a discontinuity of the whole function, f(x).

Answer 14

Anyways what do you get when you solve 3x^2+x-4=0

Answer 15

(x+1)(3x-4)=0

Answer 16

ok whick gives you x=? or x=?

Answer 17

x=-1 and x=4/-3

Answer 18

Wait how did you get (x+1)(3x-4)?

Answer 19

I think you got the + and - mixed up

Answer 20

so its (x-1) and (3x+4)?

Answer 21

3x^2+x-4
3x^2+4x-3x-4
x(3x+4)-1(3x+4)
(3x+4)(x-1)

yes.

Answer 22

so what do you get for x when you have (3x+4)(x-1)=0?

Answer 23

x=1 and x=-4/3

Answer 24

But can x=1 be a zero?

Answer 25

of f?

Answer 26

No

Answer 27

because f is actually discontinuous at x=1 because the bottom x-1 will be zero when x=1

Answer 28

right so the answer is B?

Answer 29

no

Answer 30

Oh

Answer 31

you said the function was discontinuous at x=1 and zero at x=-4/3
right?

Answer 32

Yes

Answer 33

only one choice says both of those things
and it isn't B

Answer 34

Its D

Answer 35

remember ordered pairs have the x first
and y second

Answer 36

yes
do you how to figure out the y of the discontinuity part?

Answer 37

we are done but I was just curious if you did

Answer 38

No but I haven't learned to do that yet.

Answer 39

\[f(x)=\frac{(3x+4)(x-1)}{x-1}\]
This what we get when we factor right?

Answer 40

now if you cancel the x-1's out we have
\[f(x)=3x+4 , x \neq 1 \]

Answer 41

but if you did plug in 1
you get 3(1)+4=3+4=7

Answer 42

So that is how they got (1,7) for the discontinuity point

Answer 43

Ah okay thanks for the help!

Answer 44

np

Answer 45

Can you check my other answers then?

Answer 46

i could probably check a few

Answer 47

Okay

Answer 48

What is the discontinuity of the function f(x) = the quantity of x squared minus 4 x minus 12, all over x plus 2?

(-6, 0)

(6, 0)

x (-2, -8)

(2, -4)

Answer 49

this question can be answered by you if you understand what i did

what do you think we need to do first?

Answer 50

obviously it is discontinuous where?

Answer 51

oh that x is suppose to symbolize your choice?

Answer 52

The first thing I did was set the top part equal to zero and factored then I set the bottom part equal to zero.

Answer 53

\[\frac{(x-6)(x+2)}{x+2}\] ?

Answer 54

yes thats what I got

Answer 55

and since the bottom equals 0 when x=-2
and when you cancel the (x+2)'s from the top and bottom
you have f(x)=x-6 where x does not equal -2
but if you do plug in -2 you get?

Answer 56

-8

Answer 57

right if you wanted to know what this graph looks like
notice that it is just the line y=x-6 with a hole at the point (-2,-8)
since the function does not exist there