Unit 1: Functions
What you should already know?
- graphing coordinate points
- solving basic linear equations
- x and y intercepts (finding and graphing)
- number sets (real numbers, integers, natural numbers, etc.)
- graphing linear equations
- absolute value
- solving and graphing linear inequalities
- definition of a "constant"
- I can use function notation to describe a function relation.
- I can evaluate functions for inputs from their domains.
- I can interpret statements that use function notation in terms of a context.
Introduce key features of functions including: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior.
- I can locate (on a graph) and solve for (algebraically) x and y intercepts.
- I can describe an interval in set notation and inequality notation.
- I can describe areas of increasing and decreasing on a graph.
- I can describe areas of positive or negative on a graph.
- I can find relative maximums and minimums on a graph.
- I can describe the symmetry of a graph.
- I can describe the end behavior of a graph.
Relate the domain of a function to its graph and its practical set in a real world
- I can relate the domain of a function to its graph.
- I can relate the domain of a function to its practical set in a real world problem.
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
- I can graph functions given an equation.
- I can show key features of graphs.
- I can graph piecewise-defined functions.
- I can graph step functions.
- I can graph absolute value functions.
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.
- I can compare functions given by different representations.
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), and f(x + k)
for specific values of k (both positive and negative); find the value of k given the
- I can describe the transformations possible using a constant.