Answer:
Yes all answers were correct
Step-by-step explanation:
Given : The function
is a rational function.
To check all that apply :
1) What are the asymptotes of the function
The vertical asymptotes by finding the values that make the equation undefined.
At x=0 function is undefined.
The horizontal asymptotes by comparing the degrees of the numerator and denominator or the function that approaches but never touches.
At y=0 (Also seen in the graph)
Therefore, Answer is correct X=0, Y=0
2) What is the domain of the function
The domain by finding where the equation is defined.
![D: (-\infty,0)\text{U}(0,\infty) x|x\neq 0](https://tex.z-dn.net/?f=D%3A%20%28-%5Cinfty%2C0%29%5Ctext%7BU%7D%280%2C%5Cinfty%29%20x%7Cx%5Cneq%200)
Therefore, Answer is correct that all real numbers except 0.
3) What is the behavior of the function as x approaches +infinity
At x approaches to +infinity y approaches to zero
, ![[\frac{1}{\infty}=0]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B%5Cinfty%7D%3D0%5D)
![y=0](https://tex.z-dn.net/?f=y%3D0)
Therefore, Answer is correct that y approaches zero .
4) What is the behavior of the function as x approaches zero from the right
.
At x approaches to zero y approaches to +infinity
, ![[\frac{1}{0}=\infty]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B0%7D%3D%5Cinfty%5D)
![y=+\infty](https://tex.z-dn.net/?f=y%3D%2B%5Cinfty)
Therefore, Answer is correct that y approaches +infinity.