Question

Graph the rational function f(x)=-8/x+2

Answer 1

So for this you notice that this function has an asymptote at x=-2
and an y-int at -8/2.

then notice how top is negative. so as long as x>-2 then the function will be negative
and if x<-2 then the function is positive

Answer 2

\[ f(x)=-8/x+2\rightarrow f(x)=-\frac{ 8 }{ x }+2\]
1) Find the equation of the vertical asymptote. In this case, the only denominator you have is x; set that denominator = to 0 and solve for x. Pretty obvious: x=0. This is your vertical asymptote. Your graph will not cross this vertical line.

2) Find the equation of the horizontal asymptote. There are various ways in which to do this. In this particular example, let x grow larger and larger without limit. 8/x goes to zero, leaving us with y=2. Our horizontal asymptote is y = 2.

3) Find the horizontal intercept, if there is one. To determine this, set f(x) =-8/x + 2 = to 0 and solve for x. Is that possible? If so, what is x? If you can find such x, write the horiz. intercept as (x,0) (since y=0).

4) Find the vert. intercept. To do this, attempt to set x=0 (which represents the y-axis). Is this possible? Why or why not? What is your conclusion in this case?

5) Graph the two asymptotees and the x-intercept.

6) choose a few more x values to use in locating the graph. x=0 is not possible. y=0 at x=4. So, try x = 1, 2, -1, -2.

Calculate y in each case

7) Graph these points. Sketch a curve thru them.