Question

Name the vertical asymptote(s) of the function f(x) = (x + 1)(x - 2) because:

a) x= -1 only
b) x= 2 only
c) x= -1 and x=2
d. There are no vertical asymptotes

Answer 1

The function f(x) = (x + 1)(x - 2) is a polynomial and has no vertical asymptotes, as polynomials are defined for all real x values and do not approach infinity at any finite x value.

Step-by-step explanation:

In response to the question about the vertical asymptotes of the function f(x) = (x + 1)(x - 2), we need to clarify that vertical asymptotes occur where a function approaches infinity as x approaches a particular value, but it's not defined at that value. The given function is a polynomial, specifically a quadratic function, which does not have vertical asymptotes because it is defined for all real x values. Instead, vertical asymptotes are typically associated with rational functions where the denominator can equal zero.

Therefore, the correct answer to which vertical asymptote(s) the function f(x) = (x + 1)(x - 2) has is: d. There are no vertical asymptotes.