Contents
How do you graph a function with a numerator and denominator?
How to Graph a Rational Function with Numerator and Denominator of Equal Degrees
- Sketch the vertical asymptote(s) for g(x).
- Sketch the horizontal asymptote for g(x).
- Plot the x- and y-intercepts for g(x).
- Use test values of your choice to determine whether the graph is above or below the horizontal asymptote.
How do you graph a reciprocal function?
To graph a reciprocal function in standard form, determine the domain of the function (this will also be the location of the vertical asymptote), find the horizontal asymptote, and create a table of values with some values to the right of the vertical asymptote, and some to the left of the vertical asymptote.
How do you sketch an asymptote on a graph?
Process for Graphing a Rational Function
- Find the intercepts, if there are any.
- Find the vertical asymptotes by setting the denominator equal to zero and solving.
- Find the horizontal asymptote, if it exists, using the fact above.
- The vertical asymptotes will divide the number line into regions.
- Sketch the graph.
How do you find the hole of a function?
Before putting the rational function into lowest terms, factor the numerator and denominator. If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve. The solution is the x-value of the hole.
How do you graph a function by hand?
How do you make a hole in a graph?
It is possible to have holes in the graph of a rational function. Before putting the rational function into lowest terms, factor the numerator and denominator. If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve.
What is the reciprocal of a function?
The reciprocal of a number can be determined by dividing the variable by 1. Similarly, the reciprocal of function is determined by dividing 1 by the function’s expression. Example: Given a function f(y) , its reciprocal function is 1/f(y).