Mathematics II Interpreting Functions

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Interpreting Functions

Resources

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.
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5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. tools-icon
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.
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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.
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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
function.
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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.
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