• Building Functions
F-BF Build new functions from existing functions.

MGSE9-12.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.

F-LE Construct and compare linear and exponential models and solve problems.

MGSE9-12.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

MGSE9-12.F.LE.1a Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals).

MGSE9-12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

MGSE9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

MGSE9-12.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).

MGSE9-12.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

F-LE Interpret expressions for functions in terms of the situation they model.

MGSE9-12.F.LE.5 Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a•dx ) function in terms of context. (In the functions above, “m” and “b” are the parameters of the linear function, and “a” and “d” are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.
•  Key Vocabulary

Arithmetic Sequence • Average Rate of Change • Coefficient • Constant Rate of Change • Continuous • Discrete • Domain • End Behavior • Explicit Expression • Exponential Function • Exponential Model • Expression • Even Functions • Factor • Geometric Sequence • Horizontal Shift • Interval Notation • Linear Function • Linear Model • Odd Function • Parameter • Quadratic Equation • Quadratic Function • Root • Range • Recursive Formula • Slope • Term • Vertical Translation • X-intercept • Y-intercept