• Create equations that describe numbers or relationships
• Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
• Understand the concept of a function and use function notation
• 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).
• Interpret functions that arise in applications in terms of the context
• 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.?
• Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.?
• 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.?
• Analyze functions using different representations
• Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.?
• Graph linear and quadratic functions and show intercepts, maxima, and minima.
• Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
• Build new functions from existing functions
• 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.