find the equation of the vertical asymptote of: f(x)=((x+1300)/(100-x))-3

Question

The question asks to find the equation for the vert.asympt. and I'm not sure what they mean by finding the equation?

Answer 1

Since we know it's a vertical asymptote, we know that the equation will have the form x = _______________

 

Since a vertical line doesn't pass a vertical line test, we also know that a vertical asymptote is where the function cannot exist since anything that doesn't pass a vertical line test is by definition not a function. 

 

Thus we need to look for a value for which f(x) is undefined. Since f(x) contains a fraction, we know that fractions cannot have zero for its denominator or it's undefined. Therefore, we need to look for values of x where the denominator is equal to zero. 

 

The denominator of the fraction in this case is 100-x and solving 100 - x = 0, we get that x = 100. 

 

The function becomes undefined at x=100 and that's the equation for the vertical asymptote.