Question

Use the seven step method described in the book to graph the following rational function
f(x)=(2x^2+x-3)/(2x^2-7x)
1) Determine the symmetry of the function
2) Find the y-intercept
3) Find the x-intercept
4) Find the vertical asymptotes
5) Find the horizontal asymptotes
6) Plot points between and beyond the x-intercept and the vertical asymptotes.
Type the y-coordinate for each of the following points:
-5 -2 -1 2 5
7) What should the graph look like

Answer 1

f(x) = (2x+3)(x-1) / x(2x-7)

So, the denominator is zero at x=0,7/2 making vertical asymptotes

Top and bottom are both quadratics with x^2 coefficient=2, so there is a horizontal asymptote at y = 2/2 = 1


There is no y-intercept, because f(x) is not defined for x=0

It's easy to see where y=0

f(x) is neither even nor odd, so there is no symmetry

visit wolframalpha.com to check out the graph. Just type in the function