Question

what are the zeros of the function below:

Answer 1

\[\frac{ 4x^2-36x }{ x-9 }\]

Answer 2

@ranga

Answer 3

x=0 would result in a 0, of course if x=9 there would be discontinuity.

Answer 4

so the answer choices are :
x = -9

x = 0

x= 9

x = 0 and x = 9

Answer 5

is it x = 9?

Answer 6

lol just notices i posted this is OS feedback instead of math -_-

Answer 7

No if x=9, it would result in a division by 0 and be undefined.
x=0 would result in a 0.

Answer 8

so a?

Answer 9

x = 0?

Answer 10

x = 9 is NOT in the domain of the given function.
The function is not defined at x = 9.
So the solution should not include x = 9.

Answer 11

so its a right, because thats the only solution that works

Answer 12

x = 0 is the solution. (choice B)

Answer 13

oh . i see

Answer 14

can you help me with 4 more?

Answer 15

they have to do with discontinuities

Answer 16

@ranga

Answer 17

Post one more here and I will try.

Answer 18

what is the discontinuity of the function \[f(x) = \frac{ x^2 - 3x -28 }{ x+4 }\]

Answer 19

If the denominator goes to 0 then the function is not defined because you cannot divide by zero. For what value of x does the denominator go to zero?

Answer 20

hmm 0

Answer 21

Welcome To OpenStudy! @troll?

Answer 22

im not new charlotte this is my alt acc since my main is buggy

Answer 23

is it 0 range?

Answer 24

Ah I see LOL
Well - Welcome Back!

Answer 25

thanks

Answer 26

For what value of x does x+4 become zero?

Answer 27

-4

Answer 28

Yes. x = -4 is the point of discontinuity. The function is not defined at x = -4.

Answer 29

ok so what coordinate is the discontinuity ?

Answer 30

(4, -3). is that it?

Answer 31

How did you get (4,-3)? What are the choices?

Answer 32

a. (-7, -14)

b. (7, 0)

c. (4, -3)

d. (-4, -11)

Answer 33

We just found at x = -4 there is a discontinuity. Which choice has -4 as the x coordinate?

Answer 34

d.

Answer 35

Yes. D is the answer. But if you are interested in knowing how the y-coordinate is -11 we can go over that if necessary.

Answer 36

sure

Answer 37

\[f(x) = \frac{ x^2-3x-28 }{ x+4 } = \frac{ (x-7)(x+4) }{ (x+4) } = x - 7\]
The function is not defined at x = -4.
But it is defined everywhere else.
In calculus they will teach you limit. As x approaches -4, f(x) approaches -11 because you can put x = -4 in the simplified expr3ession above where f(x) = x - 7
as x gets close to -4, f(x) will get close to (-4) - 7 = -11.
So the y value is -11 at x = -4. (-4,-11) is the point of discontinuity.

Answer 38

cool i think i grasp it now. so the x value is the one that is important to discontinuity?

Answer 39

Yes. That is where the function is undefined. The y value is not that important.

Answer 40

ok so to find the discontinuity just find the x value that makes it equal 0?

Answer 41

One way a discontinuity occurs is division by zero. If a function has an expression in the denominator, find out for what value of x the denominator will go to 0. Those x values will be the points of discontinuity.
Other ways discontinuities occur is if the function is undefined for certain values of x such as the square root function which is not defined for negative numbers. Or a logarithm function that is not defined for 0 or negative values, etc..

Answer 42

woah thats complicated… lol .

so for this expression the point of discontinuity is also -4, right? \[f (x) = \frac{ 2x^2+5x-12 }{ x+4 }\]

Answer 43

correct.

Answer 44

but this question is asking for the zeros too. the choices are

a. zero at (\[(\frac{ 3 }{ 2}, 0)\]

b. zero at

Answer 45

for choice b