# Mathematics III Interpreting Functions

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#### Resources

Interpret functions that arise in applications in terms of the context. [Include rational, square root and cube root;
emphasize selection of appropriate models.]
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. [Include rational and radical; focus on using key features to guide selection
of appropriate type of model function.]
7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology
for more complicated cases.
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing
period, midline, and amplitude.
8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the
function.
9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
by verbal descriptions).