Use the function below to answer questions 1- 5?
x^2-x-6
f(x)=---------------
x^2+x-12
1. Are there any holes in the graph of this function? If so, what is the
x-coordinate of the hole or holes?
2. Are there any vertical asymptotes when you graph this function? If so, what is the equation of the asymptote?
3. What is the domain of this function?
4. Are there any horizontal asymptotes when you graph this function? If so, what is the equation?
5. What is f(2)?
6. Does the graph of
f(x) = 2x^2+4x-1 have a horizontal asymptote?
----------------
x-2
If so, what is the equation?
7. Write a function that has a horizontal asymptote at y = 3.
--------------------------------------…
A.which of the following rational functions will produce a hole in the graph?
..........x-3
f(x)= --------
...........x+3
........x+2
f(x)=---------
.........x-2
.............1
f(x)=---------------
......(x=2)(x-2)
........(x+2)(x-2)
f(x)=----------------
..........x+2
B. at what value of x will the function g (x) have a hole?
(x+5)(x-5)(x-3)
g(x)=-----------------------
(x+5)(x+3)
5
-5
3
-3
0
C. at what value of x will the function g(x) have a vertical asymptote?
(x+5)(x-5)(x-3)
g(x)=--------------------
(x+5)(x+3)
5
-5
3
-3
0
D. what is the equation of the vertical asymptote of the function
x-1
y=------
x+3?
x=1
x=-1
x=3
x=-3
E. what is the domain
......... 3
of y=---------
.........x-4
all real numbers
all real numbers except 3
all real numbers except -4
all real numbers except 4
F. what is the domain of
x+3
y=---------
x-5
all real numbers
all real numbers except 3 and 5
all real numbers except -3 and 5
all real numbers except 5
