How do you graph #f(x)=7/(x+4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
1 Answer
Holes : None
Vertical asymptote :
Horizontal asymptote :
Explanation:
Holes are literally what they mean—a hole in a graph. It's when both numerator and denominator of the equation have an exact same factor. For example, in the equation
In our equation
Vertical asymptotes are vertical lines where the graph approaches and get closer to but NEVER touches.
To find whether there is/are vertical asymptote(s), we set the denominator of the function equal to
Our denominator of the function is
As said earlier, vertical asymptotes are vertical lines, meaning they start with
Horizontal asymptotes are horizontal lines where the graph approaches; however, it can be crossed.
The following are the rules for finding horizontal asymptotes:
In the following,
Let m be the degree of the numerator.
Let n be the degree of the denominator.

if m > n , then there is no horizontal asymptote

if m = n , then the horizontal asymptote is dividing the coefficients of the numerator and denominator

if m < n , then the horizontal asymptote is y=0
From the equation
Xintercepts are where the graph touches the xaxis. It's sort of similar to finding the vertical asymptote, but we look at the numerator instead.
We set the numerator equal to
This means that there are no xintercepts.
Yintercepts are the values of
As said, let's plug in
So there is an yintercept at
If you need more help or want to watch a video, feel free to watch this:
Sorry, I know it's kind of long!
Hope this helps!