## Unit 3 "Linear and Exponential Functions"

Key Standards

**MCC9****‐****12.A.REI.10****Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).****MCC9****‐****12.A.REI.11****Explain why the***x***‐****coordinates of the points where the graphs of the equations***y*=*f*(*x*) and*y*=*g*(*x*) intersect are the solutions of the equation*f*(*x*) =*g*(*x*); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where*f*(*x*) and/or*g*(*x*) are linear and exponential functions.**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.3****Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.****MCC9****‐****12.F.IF.4****For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.****MCC9****‐****12.F.IF.5****Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.****MCC9****‐****12.F.IF.6****Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.****MCC9****‐****12.F.IF.7****Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.****MCC9****‐****12.F.IF.7a****Graph linear functions and show intercepts, maxima, and minima.****MCC9****‐****12.F.IF.7e****Graph exponential functions, showing intercepts and end behavior.****MCC9****‐****12.F.IF.9****Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).****Build a function that models a relationship between two quantities****MCC9****‐****12.F.BF.1****Write a function that describes a relationship between two quantities.****MCC9****‐****12.F.BF.1a****Determine an explicit expression, a recursive process, or steps for calculation from a context.****MCC9****‐****12.F.BF.1b****Combine standard function types using arithmetic operations.****MCC9****‐****12.F.BF.2****Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.****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.1b****Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.****MCC9****‐****12.F.LE.1c****Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.****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.**