Evidence of Understanding

**compare the general shape and behavior of different function types**- identify
**intervals**of a function that are**increasing, decreasing, positive**or**negative**- use words, equations/inequalities, and interval notation
- generalize how intervals distinguish different function families
*(Example: quadratics always have one increasing interval and one decreasing interval)*

- predict
**end behavior**using a graph’s shape and the function’s rate(s) of change- explain why the end behavior of a periodic function is undefined

- use
**symmetry**from a function’s graph or table to distinguish function families

- identify
**identify and analyze points that determine the shape and behavior of a function’s graph**- determine
__exact__integer**zeros**and__approximate__non-integer zeros from a graph or table- recognize when a function is
**periodic**and use the repetition to describe zeros of a periodic function

- recognize when a function is
- recognize zeros (x intercepts) separate positive and negative intervals
- describe why
**critical points**(mins and maxs) separate increasing and decreasing intervals - use end behavior to distinguish
**relative**from**absolute**mins and maxs - create the graph for a given function rule using its intercepts, mins, maxs, and end behavior
- use tools strategically, especially graphing calculator features
- algebraically solve for key points of a linear or quadratic equation (using Algebra 1)

- determine
**determine a function’s family using its key points, shape, and end behavior**- describe and predict general features of critical points and zeros for each function family
*Example: cubics have at most 3 x-intercepts, quadratics always have 1 absolute min or max, etc.*

- describe characteristics of a function’s graph or sketch the possible graph of a function given its characteristics
- recognize a periodic function from its undefined end behavior, repeating points or shape

- describe and predict general features of critical points and zeros for each function family

Develop conceptual understanding:

increasing interval, decreasing interval, positive interval, negative interval, end behavior, symmetry, zero, periodic function, critical point, relative or absolute min/max

Supporting terms to communicate:

linear, absolute value, quadratic, cubic, square root, cube root, polynomial, exponential, logarithmic, rational, piecewise, step function, integer