Question

find the vertical asymptote of the graph of the function f(x)= 2x/x-4

Answer 1

The vertical asymptote is created by a value of x that the function cannot take. Since we are dealing with a fraction, you should set the denominator equal to 0, and find out what value of x will make the fraction undefined. The denominator is x - 4, so we obtain:
\[x-4 = 0\Rightarrow x = 4\]
So if x = 4, the denominator is 0, and we cant divide. Thus, the vertical asymptote is x = 4

Answer 2

What would the horizontal asymptote graph be?

Answer 3

For the horizontal asymptote, you need to learn a couple of rules. Do you know what the degree of a polynomial is?