Question

Given the function
\[f(x)=\frac{3x+1}{x-4}\]
Find:
i. the vertical asymptote(s) of the graph f
ii. the horizontal asymptote(s) of the graph f
iii. any x and y intercepts of the graph f if they exist
iv. Sketch the graph

Answer 1

I really don't know what to do for all of them...

Answer 2

i: x=4 is the only vertical asymptote because
\[\lim_{x \rightarrow 4}f(x)=\pm \infty \]

Answer 3

This is for algebra part 1 and not calculus so please don't do the derivate or integrals or use limits, thanks :).

Answer 4

ok

Answer 5

the horizontal asymptote is y =3 This is found using polynomial division

the vertical asymptote is x = 4