Precalculus

Polynomial, Power, and Rational Functions

Activities address algebraic families of functions, including polynomial functions, power functions (of the form y = xr ) and rational functions (quotients of polynomial functions). In preparation for calculus, limiting behavior is addressed, including end behavior of polynomial functions and asymptotes.

Precalculus: Polynomial, Power, and Rational Functions Activities

Title Type

End Behavior of Polynomial Functions

Students will use a slider to scroll through the graphs of power functions with a coefficient of positive and negative 1 and determine similarities and differences among the functions. Students will generalize the end-behavior properties of various power functions.

• 3279

Multiplicity of Zeros of Functions

Students will utilize graphs and equations of five polynomial functions to determine the zeros of the functions and whether the functions cross the x-axis at these zeros or just touch the x-axis at the zeros. Then students will determine the degree of the polynomial functions and the effect the degree has upon the end behavior of the functions.

• 3173

Products of Linear Functions

This lesson involves polynomial functions viewed as a product of linear functions.

• 2637

Rational Functions

In this activity, you will build a TI-Nspire file that allows you to dynamically examine the rational functions generated by quotients of linear functions.

• 2769

Exploring Vertical Asymptotes

Students will be able to determine the domain of rational functions, use algebraic concepts to determine the vertical asymptotes of a rational function, determine the removable discontinuities of a rational function, and describe the graph of a rational function given the equation.

• 3156

Crossing the Asymptote

This lesson involves determining when the graph of a rational function crosses its horizontal asymptote.

• 2778

Polynomial Rollercoaster

This lesson involves finding a cubic regression equation to model a section of roller coaster track.

• 2713