Give an example of a rational function whose graph has two vertical asymptotes: ​x​ = 2 and ​x​ = 7. Explain how you know that these are vertical asymptotes.

Question

explain and write all work.

give a example of the graph that has two vertical asymptotes of x=2 and x=7

Answer 1

Any function of x that contains 1/(x-2) and 1/(x-7) has asymptotes at x=2 and x=7 because each expression produces division by zero, which creates an infinite gradient, and an infinite gradient is a line perpendicular to the x-axis. f(x)=1/(x-2)-1/(x-7), f(x)=1/(x-2)+1/(x-7) are examples. Another example is f(x)=1/(x²-9x+14).

The graphs are respectively shown in blue, red and green.