High School Functions Common Core Resources

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).

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

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 descriptions of the relationship.

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

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph linear and quadratic functions and show intercepts, maxima, and minima

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Write a function that describes a relationship between two quantities.

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Find inverse functions.

Distinguish between situations that can be modeled with linear functions and with exponential functions.

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table.)

Observe using graphs and tables that a quantity inkling exponentially eventually exceeds a quantity increasing linearly, quadratically or more generally as a polynomial function.

Interpret the parameters in a linear or exponential function in terms of a context.