Mathematics I Interpreting Functions

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Interpreting Functions

Resources

Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and
exponential and on arithmetic and geometric sequences.]
1. 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).
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5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example,
if the function h gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers
would be an appropriate domain for the function.
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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. 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.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing
period, midline, and amplitude.
9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
by verbal descriptions).
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