The fun with functions continues. Not only do students build on their knowledge of linear- exponential- and quadratic functions- but they also transform- solve- and model functions like polynomials- rational- radical- and logarithmic functions. Other highlights include working with imaginary numbers and using statistics and probability to interpret data collected from experiments and simulations.
- Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (CCSS.Math.Content.HSA-APR.B.3)
- Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (CCSS.Math.Content.HSA-REI.A.2)
- Solve quadratic equations in one variable. (CCSS.Math.Content.HSA-REI.B.4)
- Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (CCSS.Math.Content.HSA-REI.D.11)
- Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (CCSS.Math.Content.HSA-SSE.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. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
- Find inverse functions. (CCSS.Math.Content.HSF-BF.B.3)
- 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. (CCSS.Math.Content.HSF-IF.B.4)
- Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (CCSS.Math.Content.HSF-IF.C.7)
- Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (CCSS.Math.Content.HSF-IF.C.8)
- For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. (CCSS.Math.Content.HSF-LE.A.4)
- Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. (CCSS.Math.Content.HSS-IC.B.4)
- Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (CCSS.Math.Content.HSS-ID.B.6)