Question

When looking at a rational function, Charles and Bobby have two different thoughts. Charles says that the function is defined at x = −2, x = 3, and x = 5. Bobby says that the function is undefined at those x values. Describe a situation where Charles is correct, and describe a situation where Bobby is correct. Is it possible for a situation to exist where they are both correct? Justify your reasoning.

Answer 1

so you up on rational functions?

Answer 2

YES I CAME UP WITH THE EQUATION Y=X

Answer 3

rational functions are generally the ratio of poynomials, like
\[f(x)=\frac{ p(x) }{ q(x) }\]where f(x) is the rational function, p(x) and q(x) are both polynomials.

so long as the polynomials have only non-negative, integer exponents, the rational polynomial will be defined for all values of x such that the denominator (q(x)) is NOT 0.

f(x) is NOT defined when q(x) = 0.

for example:\[f(x) = \frac{ 1 }{ x-2 }\] what makes the denominator 0?

Answer 4

i dont exactly know, can you walk me through the problem please

Answer 5

what value would x have to be in order to make the denominator 0?

Answer 6

2

Answer 7

yep, awesome! so because dividing by 0 isn't allowed, x = 2 is not defined for that function

Answer 8

ok can you help find a function that works for both their statements

Answer 9

there isn't a way a function can be both defined and undefined at the same point. it's either one or the other.

Answer 10

so how to i justify that cant be both
i have to have an explanation

Answer 11

can a gum be both sugar-free and have sugar in it?

Answer 12

i mathmatical reason
like an example of a function that wont work for both

Answer 13

make one up for each.

for one that isn't defined at x = -2, move the -2 to the other side => x+2=0

then put it on the bottom => 1/(x+2) and now you have a rational function that isn't defined when x=-2.

add the other ones using multiplcation....

\[\frac{ 1 }{ (x+2)(x-3) }\]and now you have a function that isn't defined at x=-2 and isn't defined at x=3.

get the idea?

for a function that is defined at those point, simply put them in the numerator...

(x+2)(x-3) is a function defined at x=-2 and is defined at x = 3.

Answer 14

it has to be the same equation for both

Answer 15

let me reiterate, there is NO function that is both defined and undefined at the same point.

Answer 16

ino but give me a randon equation so i can show how they cant both be right

Answer 17

hello??