12 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Browse Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### Function families share similar graphs, behaviors, and properties.

1 week

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 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 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 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

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

CORE RESOURCE

A core resource supports multiple days of instruction.

• Sorting Functions
This Core Resource reinforces what students know about functions and introduces students to polynomial and rational functions.
Resource:
Sorting Functions

This Core Resource reinforces what students know about functions and introduces students to polynomial and rational functions.

All Resources From:
• Unit 1