Question

Looking at the rational function f of x equals the quantity x minus one times the quantity x plus two times the quantity x plus four all divided by the quantity x plus one times the quantity x minus two times the quantity Bella says that the function is defined at x = –1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Who is correct? Justify your reasoning.

Answer 1

writing equations out in English makes it very hard to read.

Answer 2

can you use the equation editor?

Answer 3

how do I do that?

Answer 4

click on the equation button in the lower left of the input area

Answer 5

\[f(x)=(x-1)(x+2)(x+4)/ (x+1)(x-2)(x-4)\]

Answer 6

I couldn't find the "divide" button hahah

Answer 7

the fraction button is there, last row, on the right

Answer 8

anyway, you hopefully know we do not allow "divide by 0"
It is not done.
in your problem, if you make x certain values, the "bottom" will have a zero
and zero times anything is zero

and you will have
stuff/0
and we don't allow that.

Answer 9

@peachpi

Answer 10

Who would be right??

Answer 11

Do you understand that if you have (for example)
(x+1) in the bottom
what number (for x) makes x+1 be 0 ?

Answer 12

-1

Answer 13

and if x=-1 we will get
in the bottom
0 * (-1-2)*(-1-4)
or 0 * -3 * -5
notice the -3 and -5 don't matter, because when we multiply it out we get 0
*0 in the bottom* is not allowed

Answer 14

to prevent the divide by 0, we do not allow x=-1
then what is the answer for that expression when x=-1?
answer: we don't have an answer. It is undefined.

notice there are two other values that make the bottom 0
we don't allow those either.

can you take a guess as to who is right for this question?

Answer 15

edward!

Answer 16

Yes?

Answer 17

yes.

Answer 18

Thanks<3