Question

When looking at a rational function f of x equals the quantity x plus three times the quantity x minus two times the quantity x plus five all divided by the quantity x minus three times the quantity x plus two times the quantity x minus 5, 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. Who is correct? Justify your reasoning.

Answer 1

$f(x)=\frac{(x+3)(x-2)(x+5)}{(x-3)(x+2)(x-5)}$

Bobby is right, because at x = -2, 3, and 5, the denominator of the function equals zero, which is by definition undefined.