Understand the Problem
The question is seeking assistance with a mathematical problem, specifically related to an image that likely contains a mathematical equation or concept.
Answer
The function is \( y = \frac{1}{x} \) with domain \( x \in \mathbb{R} \setminus \{0\} \) and range \( y \in \mathbb{R} \setminus \{0\} \).
Answer for screen readers
The function is ( y = \frac{1}{x} ), with the following properties:
 Domain: ( x \in \mathbb{R} \setminus {0} )
 Range: ( y \in \mathbb{R} \setminus {0} )
 No intercepts
 Asymptotes at ( x=0 ) and ( y=0 )
Steps to Solve

Identify the equation
The equation shown is ( y = \frac{1}{x} ). This is a rational function, which means the output (( y )) is determined by the reciprocal of the input (( x )). 
Determine the characteristics of the function
To analyze this function, we need to study its properties:
 Domain: The values of ( x ) can be any real number except zero, so the domain is ( x \in \mathbb{R} \setminus {0} ).
 Range: The values of ( y ) can also be any real number except zero, giving a range of ( y \in \mathbb{R} \setminus {0} ).
 Calculate intercepts
 Yintercept: To find the yintercept, set ( x = 0 ). However, since the function is undefined at ( x = 0 ), there is no yintercept.
 Xintercept: Set ( y = 0 ). The equation cannot equal zero, thus there are no xintercepts either.

Graph the function
Sketch the graph of the function. The graph will have two branches that approach the axes but never touch them (asymptotes):
 Horizontal asymptote at ( y = 0 )
 Vertical asymptote at ( x = 0 )

Behavior of the function
The function ( y ) approaches ( 0 ) as ( x ) approaches (\pm \infty). As ( x ) approaches ( 0 ) from the right, ( y ) tends to ( +\infty ) and from the left, ( y ) tends to ( \infty ).
The function is ( y = \frac{1}{x} ), with the following properties:
 Domain: ( x \in \mathbb{R} \setminus {0} )
 Range: ( y \in \mathbb{R} \setminus {0} )
 No intercepts
 Asymptotes at ( x=0 ) and ( y=0 )
More Information
This function is an example of a hyperbola and commonly appears in calculus and various applied mathematics fields. Its properties make it important in understanding limits, asymptotic behavior, and rational functions.
Tips
 Forgetting that the function is undefined at zero, leading to incorrect conclusions about intercepts.
 Confusing the behavior of the function as ( x ) approaches zero; it goes to infinity, not to zero.