STANDARDS and OBJECTIVES
- Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
- Explain how the definition of the meaning of rational exponentsfollowsfrom extending the properties of integer exponentsto those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (51/3 )3 = 5(1/3)3 to hold, so (51/3 ) 3 must equal 5.
- Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- 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 featuresinclude: intercepts; intervals where the function isincreasing, decreasing, positive, or negative; relative maximums and minimums;symmetries; end behavior; and periodicity. ★
- 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 functionsfrom their graphs and algebraic expressionsfor them.
- . Find inverse functions. a. 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. For example, f(x) =2x 3 or f(x) = (x+1)/(x–1) for x ≠ 1.
