Mathematics I Interpreting Functions


Interpreting Functions


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).
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.
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. 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).