Find the vertical asymptotes of the following function:
f(x)={x-3}/{(x-3)(x^2-4)}.
The equation(s) of the vertical asymptote(s) of f is/are___ & ____
for vertical asymptote you are looking for those values of x which make the denominator zero, that is, that causes a division by zero
so it must be
x = 3 , x = 2, x = -2
I have that the asymptotes are -2 and 2 however for my homework I need to write an equation to find the asymptote which I do not understand...?
I wrote them as equations.
x = 3
x = 2
x = -2
I wrote it like that but the message that keeps popping up is "Unexpected character '='"
I'm using WeBWorK if that is any explanation to why I'm having issues
The flaw appears to be in the way WeBWorK accepts answers.
If it asks for the "equation" of the asymptotes, then it should accept the = sign.
try just inputting in 2, -2, and 3
To find the vertical asymptotes of a function, we need to determine the values of x for which the denominator of the function becomes zero. As a general rule, vertical asymptotes occur when the denominator of a rational function equals zero, since division by zero is undefined.
Let's find the values of x for which the denominator of the function f(x) becomes zero:
Denominator: (x - 3)(x^2 - 4)
To find the vertical asymptotes, we need to solve the equation (x - 3)(x^2 - 4) = 0.
1. (x - 3) = 0
Solving this equation, we find x = 3.
2. (x^2 - 4) = 0
This equation can be factored as (x - 2)(x + 2) = 0.
Solving this equation, we find x = 2 and x = -2.
So, the vertical asymptotes of f(x) occur at x = 3, x = 2, and x = -2.
Therefore, the equation(s) of the vertical asymptote(s) of f are x = 3, x = 2, and x = -2.