Question

Investigate several functions of the form f(x)= ax+b/cx+d. Note similarities and differences. Without graphing, how can you predict where a horizontal asymptote occur?

Answer 1

Given:-

Investigate several functions.

To find the similarites and differences.

So now we assume the functions,

`(x+1)/(x-1),(x-1)/(2x)`

now we substitute the value of 1 for x. so we get,

`\begin{gathered} (x+1)/(x-1)=(1+1)/(1-1)=(2)/(0) \\ (x-1)/(2x)=(1-1)/(2(1))=(0)/(2) \end{gathered}`

So in these two cases at first case the value of 2/0 will become infinity and there comes a hole in the graph.

But in the second case the value of 0/2 will become zero and there will not be any hole in the graph.

Like this there comes some changes between each function.