Day 04 - End Behavior/Extrema - 01.12.15

Updates
  • Quiz 1 will be on Tuesday, January 13th
  • Unit 1 Test will be on Tuesday, Jan. 20th
Bell Ringer Quiz

  1. What are functions?

    1. a mathematical relationship in which any input has one and only one output

    2. a mathematical relationship in which any input has two or more outputs

    3. a mathematical relationship in which any input has at least one output

    4. a mathematical relationship in which any output has at least one input

    5. none of the above

  2. Determine which relation is a function.

  3. If, then find f(-2).

    1. 5

    2. -3

    3. 3

    4. -1

    5. none of the above

  4. What is the x and y-intercept of ?

    1. x-intercept: (2,0) | y-intercept: (0,-8)

    2. x-intercept: (0,2) | y-intercept: (-8,0)

    3. x-intercepts: (-2,0) and (2,0) | y-intercept: (0,-8)

    4. x-intercept: (4,0) | y-intercept: (0,-8)

    5. none of the above

  5. Find the domain and range of the following:

    1. D: [-3,2) | R: (-5,2)

    2. D: (-3,2) | R: (-5,2]

    3. D: [-3,2] | R: (-5,2]

    4. D: [-3,2) | R: (-5,2]

    5. none of the above
Review
  • Intro to Functions
    • What is a function?
    • Function Notation
    • Evaluating Functions
    • Examples/Counterexamples
      • Graph
      • Table
      • Set
    • Domain/Range (using functions students covered in Algebra: linear, constant, square root, etc.)
      • Graph
      • Table
      • Set
      • Using Words
      • Compound Inequalities
      • Interval Notation
    • Intercepts
Lesson
    • Intervals Of Increasing And Decreasing (Quadratic and Absolute Value Functions)
    • Extrema
      • Relative Min/Max (Cubic Functions)
      • Absolute Min/Max (Quadratic and Absolute Value Functions)
      • Using the graphing calculator to calculate mins and maxs
        • Note: Address issue with rounding using the calculator
    • Symmetry
      • Axis of Symmetry (Quadratic and Absolute Value Functions)
    • End Behavior
    • Evaluating Functions
    • Function Operations
      • Addition, Subtraction, Multiplication, Division
      • Composition
    • Translations
        Exit Ticket
        • Posted on board at the end of the block
        Lesson Objective(s)
        • How is end behavior of a function determined?
        • How are extrema found using a graphing calculator?

        In-Class Help Requests

        Standard(s)
        • CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
        • CC.9-12.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
        • CC.9-12.F.IF.6 Interpret functions that arise in applications in terms of the context.  Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
        • CC.9-12.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
        • CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.*
        • CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.* 
        • CC.9-12.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 
        • CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
        • CC.9-12.F.BF.1c (+) Compose functions.
        • CC.9-12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
        • CC.9-12.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
        Mathematical Practice(s)
        • #1 - Make sense of problems and persevere in solving them
        • #2 - Reason abstractly and quantitatively
        • #4 - Model with mathematics
        • #5 - Use appropriate tools strategically
        • #7 - Look for and make use of structure
        Past Checkpoints