|Interpret functions that arise in applications in terms of the context. [Quadratic]|
|4. 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.
|5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.|
|6. 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. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]|
|7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology
for more complicated cases.
|a. Graph linear and quadratic functions and show intercepts, maxima, and minima.|
|b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.|
|8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the
|a. 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.
|b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of
change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and classify them as representing
exponential growth or decay.
|9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say
which has the larger maximum.