SOLUTION: a.) Find the slant asymptote of the graph of the rational function b use the slant asymptote to graph the rational function. f(x)=x^2+x-30/x-7. a.)Find the slant asymptote graph

Algebra ->  Rational-functions -> SOLUTION: a.) Find the slant asymptote of the graph of the rational function b use the slant asymptote to graph the rational function. f(x)=x^2+x-30/x-7. a.)Find the slant asymptote graph      Log On


   

Question 1002513: a.) Find the slant asymptote of the graph of the rational function b use the slant asymptote to graph the rational function. f(x)=x^2+x-30/x-7.
a.)Find the slant asymptote graph of f
b.)use the slant asymptote to graph the rational function. First determine the symmetry of the graph f.
1.)Find the y-intercept(s)
2.)Find the x-intercepts
3.)find the vertical asymptotes
4.)find the horizontal asymptote
Plot points between and beyond each x-intercept and vertical asymptote, then use the information above to graph the rational functional.
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Written correctly, you are asking for f(x)=(x^2+x-30)/(x-7).


Synthetic Division as if checking root of 7


7     |    1      1     -30 
      |           7     56
      |_____________________________________
          1       8     26

The quotient line means x%2B8%2B26%2F%28x-7%29. The rational part approaches 0 as x goes unbounded, so the slant asymtptote is highlight%28y=x%2B8%29.


Try to factorize the function.
%28%28x-5%29%28x%2B6%29%29%2F%28x-7%29

Let x=0 to find y axis intercept.
y=%280-5%29%280%2B6%29%2F%280-7%29
highlight%28y=30%2F7%29-------y-intercept.

Look at the numerator factors for the x-intercepts.
They are (5,0) and (-6,0).

Vertical asymptote is where f is undefined:
highlight%28x=7%29-----vertical asymptote


graph%28300%2C300%2C-10%2C35%2C-10%2C35%2C%28x%5E2%2Bx-30%29%2F%28x-7%29%29