SOLUTION: For the following rational equation find all the asymptotes and intercepts. Use these to graph the function. {{{f(x)=(2x^2-32)/(6x^2+13x-5)}}}

Algebra ->  Graphs -> SOLUTION: For the following rational equation find all the asymptotes and intercepts. Use these to graph the function. {{{f(x)=(2x^2-32)/(6x^2+13x-5)}}}      Log On


   

Question 1176662: For the following rational equation find all the asymptotes and intercepts. Use these to graph the function.
f%28x%29=%282x%5E2-32%29%2F%286x%5E2%2B13x-5%29
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%282x%5E2-32%29%2F%286x%5E2%2B13x-5%29
f%28x%29=%282x%5E2-32%29%2F%28%283x-1%29%282x%2B+5%29%29
asymptotes
Vertical:
%283+x+-+1%29+%282+x+%2B+5%29=0
3+x+-+1=0
3+x+=1
x+=1%2F3
%282+x+%2B+5%29=0
x+=-5
2+x+=-5%2F2
Vertical asymptotes are:
x=-5%2F2 and x=1%2F3

Horizontal: take coefficients of variable with highest degree , 2%2F6
y=2%2F6
y=1%2F3+

intercepts:
to find x-intercepts, set numerator to zero
2x%5E2-32=0
2%28x%5E2-16%29=0
2%28x%5E2-4%5E2%29=0
2%28x-4%29%28x%2B4%29=0
=>x=4 or x=-4
x-intercepts are: (4,0),(-4,0)

to find y-intercepts, set x=0
f%28x%29=%282%2A0%5E2-32%29%2F%286%2A0%5E2%2B13%2A0-5%29=-32%2F-5=32%2F5
y-intercept is (0,32%2F5)