Which point is NOT on the graph of y=-(2)/(x) ? A. (-(1)/(2), 4) B. (-1,2) C. (2,-1) D. (8,-(1)/

step 1 The equation we're looking at here is y equals negative 2 over x. Okay, and it wants to know whi

Which point is NOT on the graph of y=-(2)/(x) ? A....

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Key Concepts

Rational Functions

Rational functions are functions that can be expressed as the ratio of two polynomials. They often have features such as vertical and horizontal asymptotes, and they can model various types of behavior depending on the degrees of the numerator and denominator. Understanding these functions includes analyzing their domain, asymptotic behavior, and the effects of constants and variables in the expression.

Reciprocal Functions

A reciprocal function is a specific type of rational function where the variable, or a modification of the variable, appears in the denominator, such as 1/x or variations thereof. These functions are characterized by their hyperbolic graphs and distinctive asymptotic properties. Recognizing the general features of reciprocal functions helps in understanding their graphs and behavior as x approaches zero or infinity.

Verifying Points on a Graph

Verifying whether a point lies on a graph involves substituting the x-coordinate of the point into the function and checking if the resulting output matches the y-coordinate of the point. This method of substitution is a fundamental tool in algebra and analytic geometry used to validate solutions, understand graphs, and confirm the consistency of given points with a particular function.

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