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 that they are both correct? Justify your reasoning.

Answer 1

Consider the function \(f(x) = \dfrac{1}{(x+2)(x-3)(x-5)}\) Is this function defined for \(x=-2,3,\) or \(5\)?

Answer 2

and why?

Answer 3

yes those are the vertical asymptotes? and the zeros/roots

Answer 4

NO! It is not defined for \(x=-2, 3, \) and \(5\). What happens if you plug in 3?

Answer 5

when i graph the function on a graphing calculator the table says error, for -2,3,5.
3 doesnt work

Answer 6

right, \(\dfrac{1}{(-2+3)(3-3)(5-3)}=\dfrac{1}{1*0*2}=\dfrac{1}{0}\) YIKES

Answer 7

So a function is not defined for a number that causes us to divide by \(0\).

Answer 8

so there is no time when the both of them can be correct??