Understands and applies functions
The concept of function is central to the study of algebra. A function can be thought of as a rule (or equation), like y = 3x + 4 or f(x) = 5x2 + 7, a table of (x, y) pairs, or a graph in the plane, such as a line or parabola. Functions can be used to model patterns of change between quantitative variables, including in real world situations. Often when modeling or solving problems with functions, students will create, analyze, and manipulate algebraic expressions and solve equations and inequalities. Students should also understand and analyze relations that are not functions (such as x2 + y2 = 5 and x = y2).
Students' experiences with function should include analysis of families of functions (linear, quadratic, other polynomial, exponential, trigonometric, rational, logarithmic, and piecewise). Analysis of these functions should include: zeros, maximum and minimum, domain and range, global and local behavior, intercepts, rates of change, and asymptotes. Students should be able to recognize, represent, compare/contrast, transform, compose, and find inverses of functions. They should represent functions in multiple ways: symbolically (explicitly and recursively), graphically, numerically, and verbally, and understand the connections among these representations.