Coordinate Algebra Introduction to Functions Unit
This unit is an introduction to linear and exponential functions. The goals of this unit are to:
Primary CCGPS Coordinate Algebra Standards addressed in this unit:
This unit consists of four lessons:
- Introduce linear functions and their graphs
- Introduce function notation and related vocabulary
- Introduce exponential functions
- Provide a comparison between linear and exponential growth
- Enable students to describe how parameters effect the graphs of linear and exponential functions
- Enable students to construct of linear and exponential functions given either graphs of points or input and output values
Primary CCGPS Coordinate Algebra Standards addressed in this unit:
- MCC9‐12.F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
- MCC9‐12.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- MCC9‐12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple
- MCC9‐12.F.BF.1 Write a function that describes a relationship between two quantities. ★
- MCC9‐12.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
- MCC9‐12.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
- MCC9‐12.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
- MCC9‐12.F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input‐output pairs (include reading these from a table).★
- MCC9‐12.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly. ★
- MCC9‐12.F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
- MCC9‐12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
- MCC9-12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
This unit consists of four lessons:
This unit was created by Carey Farr, Cristina Tyris, Abby Miner, and Elizabeth Gieseking in EMAT 6700 at the University of Georgia, May 2015.