Question

find the slant asymptote of the graphof the rational function.

1.f(x)=x^2-x-2/x-7
y=?

2. determine the symmetry of the graph of f.
a. the graph has y-axis symmetry f(-x)=f(x)
b. the graph has orgin symmetry f(-x)= -f(x)
c. the graph has both y-axs and orgin symmetry
d. the graph has neither y-axis nor orgin symmetry

3. find the y-intercepts
4. find the x-intercepts
5. find the vertical intercepts
6. find the horizontal asymptotes

please show work

Answer 1

since f(x) = x + 6 + 40/(x-7)

f(x) = x+6 plus an amount that gets small as x gets large.

So, the slant asymptote is y=x+6

go to wolframalpha.com and type in

(x^2-x-2)/(x-7)

and it will show the graph, making the other answers easy to decide.