Algebra2-Functions
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Algebra2-Functions

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This is a review/basic lesson on how to work with functions.

This is a review/basic lesson on how to work with functions.

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Algebra2-Functions Algebra2-Functions Presentation Transcript

  • Algebra II
    Functions
  • Time for A Movie!
    View Video
  • Math in The Movies
    How can we relate what just happened to Indiana Jones to math?
    Lets think about the massive rock that Indiana was running away from: Could we graph the changing positions of both Indiana and the rock as time passes? Why?
  • Lets Make A Graph
    First copy these points onto your graph paper. Then, we will graph the positions of Indiana and the rock with coordinates (ordered pairs) of the form (x,y) where: X=Time(s) and Y=Distance from the exit(m)
    Indiana’s Position
    (0,25)
    (5,19)
    (9,16)
    (15,9)
    (20,4)
    (25,0)
    (30,-5
    The Rock’s Position
    (0,26)
    (5,21)
    (9,17)
    (15,12)
    (20,6)
    (25,1)
    (30,0)
  • Plotting Points
    First choose two different colored pencils: One for Indiana’s position and another for the rock’s position.
    Lets plot the first position of each object together.
    The red dot represents the rock’s position and the blue dot represents Indiana’s position at time 0.
    The rock: (0,26)
    Indiana: (0,25)
  • Complete the Graph
    Plot the remaining points on your graph
  • What is A Function?
    The sets of ordered pairs that we graphed earlier are relations.
    The domain of a relation is the set of all first coordinates (x-coordinates).
    The range is the set of all second coordinates (y-coordinates).
    A function is a special type of relation in which each element of the domain is paired with exactly one element from the range.
  • Are There different Types of Functions?
    Discrete Functions
    Have a domain with a finite set of points.
    Can be represented by several points.
    Continuous Functions
    Have a domain with and infinite number of elements.
    Can be represented as a line.
  • Are You Sure That’s a Function?
    You can use the vertical line test to determine if a relation is a function.
    A relation can only be a function if a vertical line, drawn through any point in the relation, passes through the relation only once.
  • Lets Find the Domain and Range of Our Data.
    First lets find the domain of Indiana’s position.
    Now find the domain of the rock’s position.
    Lets find the range of Indiana.
    The Rock?
    {0,5,9,15,20,25,30}
    {0,5,9,15,20,25,30}
    {25,19,16,9,4,0,-5}
    {26,21,17,12,6,1,0}
  • We Can Draw Diagrams That Relate the Domain and Range of the Objects:
    Indiana
    The Rock
    0
    5
    9
    15
    20
    25
    30
    0
    5
    9
    15
    20
    25
    30
    25
    19
    16
    9
    4
    0
    -5
    26
    21
    17
    12
    6
    1
    0
    • Insert lines that connect each domain point to its corresponding range point according to the ordered pairs.
    • Do these diagrams fit the definition of a function? How?
  • What Type of Function is Our Graph?
    It is a discrete function, but we can make it resemble a continuous function.
    Draw a line of best fit for each set of points.
    Does each line pass the vertical line test?
    Indiana Jones escapes the cave at the time of 25 seconds. How does the graph support the fact that he is not flattened?
  • Equations of the Lines
    The best-fit line of Indiana’s position can be roughly represented by the equation y=25-x.
    The best-fit line of the rock’s position can be represented by y=26-x.
    Use our given domain from before to create a table of values where range is represented by the y value of the equations.
    Do these points correspond to a function? For what reasons?
  • What is a Function Again???
    • Explain why these sets of points represent functions.
    • Can you think of ways functions may be used?
    • Why are the domain and range of a function important?
    • How can functions predict the future?
    • Can you think of situations where there are functions present?
  • Work Time
    Tomorrow we will continue with linear equations which represent a type of continuous function.
    Are there any further questions about functions?
    You may keep your graph and turn it in with your homework tomorrow.
    Please spend the rest of the class period working on the worksheet. You may work with a partner on it, but you each must complete your own paper.
    If you do not finish please have it done for tomorrow along with the homework from section 2.1: #16-58 even.