SOLUTION: make a graph of f(x= x+3/x^2+x-12. List all asymptotes and the domains and the x,y intercepts

Algebra ->  Trigonometry-basics -> SOLUTION: make a graph of f(x= x+3/x^2+x-12. List all asymptotes and the domains and the x,y intercepts      Log On


   

Question 1137488: make a graph of f(x= x+3/x^2+x-12. List all asymptotes and the domains and the x,y intercepts
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

make a graph of
f%28x%29=+%28x%2B3%29%2F%28x%5E2%2Bx-12%29
f%28x%29=+%28x%2B3%29%2F%28x%5E2-3x%2B4x-12%29
f%28x%29=+%28x%2B3%29%2F%28%28x%5E2-3x%29%2B%284x-12%29%29
f%28x%29=+%28x%2B3%29%2F%28x%28x-3%29%2B4%28x-3%29%29
f%28x%29=+%28x%2B3%29%2F%28%28x+%2B+4%29+%28x+-+3%29%29


asymptotes:
Horizontal asymptote: y=0
%28x+%2B+3%29%2F%28x%5E2+%2B+x+-+12%29-%3E0 as x-> ± infinity
Vertical asymptotes: x=-4 and x=3
%28x+%2B+3%29%2F%28x%5E2+%2B+x+-+12%29-> ± infinity as x-%3E-4
%28x+%2B+3%29%2F%28x%5E2+%2B+x+-+12%29-> ± infinity as x-%3E3
domain:
{ x element R : x%3C%3E-4 and x%3C%3E3 }
the x intercepts:
x%2B3=0 =>x=-3
the x intercepts:( -3,0)
the y intercept:
f%280%29=+%280%2B3%29%2F%280%5E2%2B0-12%29=3%2F-12=-1%2F4
(0, -1%2F4)





Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
here's your graph.

$$$

the equation that was graphed is y = x^2/(x^2+x-12)

you have vertical asymptotes at x = -4 and x = 3.

that's because x^2 + 2x - 12 factors into (x+4) * (x-3.

the denominator becomes 0 when x = -4 and x = 3.

those value of x are where your vertical asymptotes are.

since no real value of y is possible when x = -4 and x = 3, those values of x are not in the domain.

therefore, the domain is all real values of x except at x except at x = -4 and x = 3.

the range is all real values of y.

the x intercept is the value of x when the value of y is equal to 0.

to find those values of x, set y = 0 and solve for x.

y = x^3 / (x^2 + x - 12) becomes x^3 / (x^2 + x - 12) = 0 when y = 0.

multiply both sides of the equation by (x^2 + x - 12) and you get x^3 = 0

solve for x to get x = 0.

that's your x-intercept.

to solve for the y-intercept, make x = 0 and you get y = x^3 / (x^2 + x - 12) becomes y = 0 / (-12) which becomes y = 0.

the y-intercept is at x = 0.

your x-intercept is at (0,0).

your y-intercept is at (0,0).