Mathematics | Course : Model Algebra I (Traditional Pathway)
Domain - Interpreting Functions
Cluster - Analyze functions using different representations.
[AI.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.
[AI.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 (range) of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
[AI.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, quadratic, exponential, and absolute value functions. Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph.
[AI.F-LE.A.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.*
[AII.F-IF.C.7.c] -
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.*
[AII.F-TF.B.5] -
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*