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This algebra 2 math tutorial from NutshellMath offers homework help graphing rational functions. Rational functions are functions that can be expressed as the quotient of two polynomials. The algebraic representation of this form is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial expressions, and Q(x) cannot equal zero.
Rational functions are said to be 'defined' in the domain, or set of values for x, where Q(x) is non-zero. Rational functions will have a vertical asymptote at values for x that cause Q(x) to equal zero.
This tutorial explores the example of hyperbolas, which are rational functions of the form y = (ax+b)/(cx+d). The teacher first finds the vertical asymptote of the graph, at the value for x where the denominator of the polynomial expression equals zero. Next, the teacher finds the horizontal asymptote, where y is equal to the ratio of the coefficients of x in the numerator and denominator.
To graph the hyperbola, first draw a Cartesian coordinate system and sketch the asymptotes. Next, plot several points by picking values for x and solving for y. Then it is possible to sketch the graph.
Graphing functions can give us general idea of the behavior of a function over a range of values; help us make predictions on the future or past behavior of the function.Hyperbolas are just one type of rational function. Other types will have different graphs, but learning to find asymptotes and plotting points to define a curve are the essential steps in graphing rational functions.
This algebra 2 math tutorial from NutshellMath offers homework help graphing rational functions. Rational functions are functions that can be expressed as the quotient of two polynomials. The algebraic representation of this form is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial expressions, and Q(x) cannot equal zero.
Rational functions are said to be 'defined' in the domain, or set of values for x, where Q(x) is non-zero. Rational functions will have a vertical asymptote at values for x that cause Q(x) to equal zero.
This tutorial explores the example of hyperbolas, which are rational functions of the form y = (ax+b)/(cx+d). The teacher first finds the vertical asymptote of the graph, at the value for x where the denominator of the polynomial expression equals zero. Next, the teacher finds the horizontal asymptote, where y is equal to the ratio of the coefficients of x in the numerator and denominator.
To graph the hyperbola, first draw a Cartesian coordinate system and sketch the asymptotes. Next, plot several points by picking values for x and solving for y. Then it is possible to sketch the graph.
Graphing functions can give us general idea of the behavior of a function over a range of values; help us make predictions on the future or past behavior of the function.Hyperbolas are just one type of rational function. Other types will have different graphs, but learning to find asymptotes and plotting points to define a curve are the essential steps in graphing rational functions.