La. Admin. Code tit. 28 § CLXXI-2105

Current through Register Vol. 50, No. 8, August 20, 2024

Section CLXXI-2105 - Functions

A. 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).

B. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

C. Recognize that sequences are functions whose domain is a subset of the integers. Relate arithmetic sequences to linear functions and geometric sequences to exponential functions.

D. For linear, piecewise linear (to include absolute value), quadratic, and exponential functions that model 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; and end behavior.)

E. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F. Calculate and interpret the average rate of change of a linear, quadratic, piecewise linear (to include absolute value), and exponential function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

G. Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

1. Graph linear and quadratic functions and show intercepts, maxima, and minima.

2. Graph piecewise linear (to include absolute value) and exponential functions.

H. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

1. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

I. Compare properties of two functions (linear, quadratic, piecewise linear [to include absolute value] or exponential) each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Example: Given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

J. Write a linear, quadratic, or exponential function that describes a relationship between two quantities.

1. Determine an explicit expression, a recursive process, or steps for calculation from a context.

K. 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). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graphs that include cases where f(x) is a linear, quadratic, piecewise linear (to include absolute value), or exponential function.

L. Distinguish between situations that can be modeled with linear functions and with exponential functions.

1. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

2. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

3. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

M. 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).

N. Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

O. Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.

La. Admin. Code tit. 28, § CLXXI-2105

Promulgated by the Board of Elementary and Secondary Education, LR 421058 (7/1/2016).

AUTHORITY NOTE: Promulgated in accordance with R.S. 17.6, R.S. 17:24.4, and R.S. 17:154.