Pre-Calculus 12 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Pre-calculus 12 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
RF01 Students will be expected to demonstrate an understanding of operations on, and compositions of, functions. [CN, R, T, V]
RF01.01 Sketch the graph of a function that is the sum, difference, product, or quotient of two functions, given their graphs.
RF01.02 Write the equation of a function that is the sum, difference, product, or quotient of two or more functions, given their equations.
RF01.03 Determine the domain and range of a function that is the sum, difference, product, or quotient of two functions.
RF01.04 Write a function h(x) as the sum, difference, product, or quotient of two or more functions.
RF01.05 Determine the value of the composition of functions when evaluated at a point, including f[f(a)], f[g(a)], and g[f(a)].
RF01.06 Determine, given the equations of two functions f(x) and g(x), the equation of the composite function f[f(x)], f[g(x)], and g[f(x)], and explain any restrictions.
RF01.07 Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function f[f(x)], f[g(x)], and g[f(x)].
RF01.08 Write a function h(x) as the composition of two or more functions.
RF01.09 Write a function h(x) by combining two or more functions through operations on, and compositions of, functions
Additional Resources and Activities for RF01 (operations on, and compositions of, functions ):
Note: Indicator RF01.09 (Write a function h(x) by combining two or more functions through operations on, and compositions of, functions) has been removed from curriculum.
Vending Machines - A variety of different vending machines to describe different types of functional relationships... constant functions, one-to-one functions, non-functions, etc. Great photo resources from Christopher Danielson.
Composite Functions Match-Up - A practice matching sheet for composite functions from Dr. Austin Maths. Solutions.
Combining Functions Row Game - A "row game" is an activity for students to work with a partner to evaluate a series of expressions. The expressions are written in two columns. One student evaluates the expressions in the left column and the other student evaluates the expressions in the right column.
Memes > Quiz (Composition of Functions) - Students use visual imagery to demonstrate their understanding of composition of functions. A google slides for directions and examples and a rubric from Mary Williams. Also a google slides that could be used for doing this project virtually or online.
Self - Directed Lessons for Function Operations (Chapter 10 in Pre-Calculus 12 (McAskill et a. 2012) ) - *Updated June 2025*
These Desmos Activities can be assigned to students for independent exploration once Unit 1: Function and Transformations and Unit 2: Radical Functions have been completed.
Desmos Activity: Sums and Differences of Functions - This activity introduces students to the idea of combining functions using addition and subtraction (Based on Ch. 10.1: Sums and Differences of Functions from Pre-Calculus 12 (McAskill et al. 2012)).
Desmos Activity: Products and Quotients of Functions - This activity introduces students to the idea of combining functions using multiplication and division (Based on Ch. 10.2: Products and Quotients of Functions from Pre-Calculus 12 (McAskill et al. 2012)).
Desmos Activity: Composite Functions - This activity introduces students to the idea of combining functions using composition to create new functions (Based on Ch. 10.3: Composition of Functions from Pre-Calculus 12 (McAskill et al. 2012)).