Question 62284
Find the vertical and horizontal asymptotes of y=(5x^2-8x+1)/(2x^2-5x-12)
When the degree of the numerator and denominator are the same, the horizontal asymptote will be at their leading coefficients: y=5/2
There is a vertical asymptote anywhere that it is undefined once it's factored and simplified.
{{{y=(5x^2-8x+1)/((2x^2-8x+3x-12))}}}
{{{y=(5x^2-8x+1)/(2x(x-4)+3(x-4))}}}
{{{y=(5x^2-8x+1)/((2x+3)(x-4))}}}
There are two vertical asymptotes:
2x+3=0 and x-4=0
2x=-3 and x=4
x=-3/2 and x=4
Here's what it looks like:
{{{graph(300,200,-10,10,-10,10,(5x^2-8x+1)/(2x^2-5x-12))}}}
Happy Calculating!!!