La. Admin. Code tit. 28 § CLXXI-2305
Current through Register Vol. 50, No. 11, November 20, 2024
Section CLXXI-2305 - FunctionsA. 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; and periodicity.)B. 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.C. 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 square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.2. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.3. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.D. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 1. Use the properties of exponents to interpret expressions for exponential functions. Example: Identify percent rate of change in functions such as y=(1.02)t, y=(0.97)t, y= (1.01)12t, y= (1.2)t/10 and classify them as representing exponential growth or decay.
E. Compare properties of two functions 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.
F. Write a function that describes a relationship between two quantities. 1. Determine an explicit expression, a recursive process, or steps for calculation from a context.2. Combine standard function types using arithmetic operations. Example: Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
G. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.H. 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.I. Find inverse functions. 1. Solve an equation of the form f(x)=c for a simple function f that has an inverse, and write an expression for the inverse. Example: f(x)=2x3 or f(x)= (x+1)/(x-1) for x [NOT EQUALS TO] 1
J. Given a graph, a description of a relationship, or two input-output pairs (include reading these from a table), construct linear and exponential functions, including arithmetic and geometric sequences, to solve multistep problems.K. For exponential models, express as a logarithm the solution to ab(ct)=d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.L. Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.M. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.N. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.O. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.P. Prove the Pythagorean identity sin2([THETA]) + cos2([THETA])=1 and use it find sin([THETA]), cos([THETA]), or tan([THETA]) given sin([THETA]), cos([THETA]), or tan([THETA]) and the quadrant.La. Admin. Code tit. 28, § CLXXI-2305
Promulgated by the Board of Elementary and Secondary Education, LR 421059 (7/1/2016).AUTHORITY NOTE: Promulgated in accordance with R.S. 17.6, R.S. 17:24.4, and RS. 17:154.