Curriculum

Unit Outlines Standards

Accelerated Mathematics 1 Version: CPS 08/09

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Unit Name: 01 Characteristics of Functions

Essential Question

What is a function?

Enduring Understanding

  • Functions have three parts: (i) a domain, which is the set of inputs to the function, (ii) a range, which is the set of outputs, and (iii) some rule or statement of correspond indicating how each input determines a unique output.
  • The domain and rule of correspondence determine the range.
  • Graphs are geometric representations of functions.
  • Functions are equal if and only if they have the same domain and rule of correspondence.
  • Function notation provides an efficient way to talk about functions, but notation is just that, an efficient way to talk about functions. The variables used to represent domain values, range values, and the function as a whole is arbitrary. Changing variable names does not change the function.
  • Logical equivalence is a concept that applies to the form of a conditional statement. Every conditional statement and its contrapositive are logically equivalent. Given a true conditional statement, whether the converse or inverse of the conditional statement is also true depends on the content of the statement. The converse and inverse forms are not logically equivalent to the original conditional form.
  • The definitions of even and odd symmetry for functions are stated as algebraic conditions on values of functions, but each symmetry has a geometric interpretation related to reflection of the graph through one or more of the coordinate axes.
  • For any graph, rotational symmetry of 180 degrees about the origin is the same as point symmetry of reflection through the origin.
  • Topic 1

    Characteristics of Functions

  • Functions
  • Parent graphs of 6 basic functions
  • Discrete vs. Continuous functions
  • Domain and Range
  • Topic 1 Standards and Elements


    MA1A1.a.
    MA1A1.b.
    MA1A1.d.
    MA1A1.e.

    Topic 2

    Logical Equivalence

  • Conditional statements
  • Negation
  • Converse
  • Inverse
  • Contrapositive
  • Topic 2 Standards and Elements


    MA1G2
    MA1G2.a.
    MA1G2.b.

    Topic 3

    Average rate of change

    Topic 3 Standards and Elements


    MA1A1.g.

    Topic 4

    Sequences

  • Whole number domains
  • Closed and Recursive definitions of functions
  • Restricted domains
  • Topic 4 Standards and Elements


    MA1A1.b.
    MA1A1.e.
    MA1A1.f.

    Topic 5

    Transformations

  • Vertical and Horizontal shifts
  • Stretches and shrinks
  • Reflections
  • Even and Odd functions
  • Topic 5 Standards and Elements


    MA1A1
    MA1A1.c.
    MA1A1.d.
    MA1A1.h.

    Unit Vocabulary

      Word Wall
    • average rate of change
    • conditional statement
    • converse
    • contrapositive
    • domain
    • end behavior
    • inverse
    • logical equivalence
    • odd function
    • negation
    • function notation
    • intervals of increase
    • invervals of decrease
    • range
    • recursive
    • shrink
    • even function
    • zeros
    • horizontal shift
    • stretch
    • symmetry
    • transformation
    • vertical shift

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