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.
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writing equations out in English makes it very hard to read.
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
and we don't allow that.
Who would be right??
Do you understand that if you have (for example)
(x+1) in the bottom
what number (for x) makes x+1 be 0 ?
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
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?