The purpose of this task is to extend the Fundamental Theorem of Algebra from quadratic functions to cubic functions. The task asks students to use graphs and equations to find roots and factors and to consider the relationship between them. Students will also consider quadratic and cubic functions with multiple real roots and imaginary roots.

CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

CK-12's Texas Instrument Calculus Student Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

CK-12 Calculus Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Calculus Student Edition. The solution guide is available upon request.

This lesson unit is intended to help teachers assess how well students are able to: articulate verbally the relationships between variables arising in everyday contexts; translate between everyday situations and sketch graphs of relationships between variables; interpret algebraic functions in terms of the contexts in which they arise; and reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.

The purpose of this task is to solidify student understanding of how the degree of the polynomial function impacts the rate of change and end behavior. By comparing the values of expressions with ‘extreme’ values, students will be able to:
• Understand that the degree of the polynomial is the highest valued whole number exponent and that this term determines the end behavior (regardless of the other terms in the expression).
• Determine that the higher the degree of a polynomial, the greater the value as F approaches infinity. Understand that while the highest degree polynomial has the greatest value as F → ∞, that exponential functions have the greatest rate of change, and therefore the greatest value when F becomes very large.
• Identify differences between even and odd degree functions. In this task, students will know the end behavior for odd degree functions (as F → −∞, H(F) → −∞ and that both even and odd degree polynomial functions as F → ∞, H(F) → ∞) as long as the co-efficient is positive and realize that the opposite is true if the co-efficient is negative.

This is a lesson on L'Hospital's rule which is an AP Calculus AB/BC topic. Students will learn about indeterminate forms and how to use a derivative to determine the limit.

As students prepare to work with algebraic expressions, either with operations (add, subtract, multiply, or divide) or when making connections to constant, linear, and/or quadratic functions, it is important that students can name basic polynomial expressions as monomials, binomials, or trinomials, During this activity students will learn how to name these polynomials through watching a video, practice naming polynomials through a sorting activity, and then complete five-formative assessment questions.

This lesson unit is intended to help teachers assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in: recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials; and recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).