Unit 1:Graphing Functions

Unit 1

Key Learning:
Functions describe situations where one quantity determines another.  Because we continually make theories about dependencies between quantities in nature and society, functions are important tools in the construction of mathematical models.  The graph of a function is a useful way of visualizing the relationship the function models, and manipulating a mathematical expression for a function can throw light on the function’s properties.

Unit Essential Questions:
Why should functions be analyzed graphically?

Concept 1:
Functions (A1, 1-4)		 Concept 2:
Transforming Functions (1-6, 1-7)
 Concept 3:
Graphing Functions (1-2, 1-5) 		Concept 4:
Piecewise Functions & Function Inverses (1-9) 

Lesson Essential Questions:

How are inequality and interval notation related? 

How do you describe the domain and range of relations and functions?

Lesson Essential Questions:

How are the parent graphs of functions similar and different from one another?

How do rigid and non-rigid transformations alter the equation and graph of a function?

 Lesson Essential Questions:

How is symmetry useful when differentiating between functions that are even, odd, or neither?

How do you identify the zeros of a function algebraically, graphically, or from a table of ordered pairs?

How are intervals of increasing, decreasing, and constant related to extrema?

How do discontinuities effect the end behavior of a function?

Lesson Essential Questions:

How are piecewise functions created, analyzed, and compared?

How are piecewise functions constructed and interpreted to model real world situations?

How are functions related to their inverses?

Vocabulary:
bounded, unbounded, interval notation, relation, function, domain, range, vertical line test

Vocabulary:
cube root function, asymptote, piecewise function, step function, translation, reflection, dilation, rigid and non-rigid transformations

Vocabulary:
zeros, symmetry, extrema, even and odd functions

Vocabulary:
inverse function, one-to-one, horizontal line test