Mathematics | Course : Model Mathematics I (Integrated Pathway)
Domain - Interpreting Functions
Cluster - Analyze functions using different representations.
[MI.F-IF.C.7.e] - Graph exponential functions, showing intercepts and end behavior.*
- Exponential function
A function of the form y = a •bx where a > 0 and either 0 < b < 1 or b > 1. The variables do not have to be x and y. For example, A = 3.2 • (1.02)t is an exponential function.
[MI.F-IF.A.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).
[MI.F-BF.B.3] -
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Include linear and exponential models. (Focus on vertical translations for exponential functions). Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph.
[MI.F-LE.A.3] -
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.*
[MIII.F-IF.C.7.c] -
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.*
[MIII.F-TF.B.5] -
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*