SOLUTION: Explain how to Find any horizontal and vertical asymptotes and any holes that may exist for the rational function. Draw a graph, including any x and y intercepts: y=((x^2)+7x+1

Question 895387: Explain how to Find any horizontal and vertical asymptotes and any holes that may exist for the rational function. Draw a graph, including any x and y intercepts:
y=((x^2)+7x+12)/(x+4)
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
That rational equation has no horizontal asymptotes. Notice x unbounded approaches either negative infinity or positive infinity, based on y approaching .

Just to be more certain in possible vertical asymptotes, factorize the numerator if possible.
(x+3)(x+4)-----------the numerator.
NO vertical asymptote, because

-
Your rational equation is the line but MISSING x=-4. There is no included point at x=-4. You can call this a hole in the line. (This cannot be seen well on most graphs produced through software, but you can represent what you want in a manually drawn graph or sketch.)

No real use in looking for slant asymptote, since the rational equation is already a line (missing one point.)
RELATED QUESTIONS
What is an equation of a rational function without any "holes", vertical asymptotes, or... (answered by Fombitz)

find the vertical, horizontal, and oblique asymptotes, if any, for the following rational (answered by stanbon)

Find the vertical, horizontal, and oblique asymptotes, if any, as well as any holes, of... (answered by venugopalramana)

f(x)=((x-1)/(x^2 x-12)) factor the function and find the domain and any holes find any... (answered by lynnlo)

I have a homework question that states: graph the rational function. Find any vertical... (answered by scianci)

Given the rational function f(x)=2x/x+4 I need to find the domain,find the equation of... (answered by edjones)

For each rational function, identify any holes or horizontal or vertical asymptotes of... (answered by stanbon)

find the rational fraction, identify any holes or horizontal or vertical asymptotes of... (answered by richard1234)

Graph the rational funxtion f(x)=x^2+5x-6/x^2+2x-3. indentify the vertical and horizontal (answered by Fombitz)