1. ![x\in (-\infty, -1)\cup (-1,\infty)](/tpl/images/0313/6340/2521e.png)
2. ![x=-1](/tpl/images/0313/6340/66413.png)
3. ![x=\dfrac{1}{2}](/tpl/images/0313/6340/6a253.png)
4. ![(0,-1)](/tpl/images/0313/6340/ea4bc.png)
5. ![y=2](/tpl/images/0313/6340/80bdd.png)
6. There are no holes for this function.
7. There are no oblique asymptotes.
Step-by-step explanation:
Consider the function
The denominator of the fraction includes the expression
Since the denominator cannot be equal to 0, then
![x+1\neq 0,\\ \\x\neq -1.](/tpl/images/0313/6340/a5d33.png)
Thus, the range is ![x\in (-\infty, -1)\cup (-1,\infty)](/tpl/images/0313/6340/2521e.png)
and line
is a vertical asymptote.
The roots of the function are:
![f(x)=0\Rightarrow 2-\dfrac{3}{x+1}=0,\\ \\\dfrac{2x+2-3}{x+1}=0\Rightarrow 2x+2-3=0,\\ \\2x-1=0,\\ \\\2x=1,\\ \\x=\dfrac{1}{2}.](/tpl/images/0313/6340/cc5c0.png)
When ![x=0,](/tpl/images/0313/6340/0e397.png)
![f(0)=2-\dfrac{3}{0+1},\\ \\f(0)=2-3=-1.](/tpl/images/0313/6340/cad12.png)
Point (0,-1) is y-intercept.
The line
is a horizontal asymptote.
There are no holes for this function.
There are no oblique asymptotes.
![domain: v.a: roots: y-int: h.a: holes: o.a: also, draw on the graph.](/tpl/images/0313/6340/7e6ce.jpg)