Lesson 1 - Power Functions

• Predict the end behaviour of a polynomial function

  1. Identify if the equation is even or odd by observing the highest degree

  2. Determine if the leading coefficient is positive or negative

  3. Use end behaviour to state which quadrants the ends are in

  4. Use approaching notation to indicate which direction the ends are going in

     Ex. Predict the end behaviour of y = x³ - 2x³ - 3x

     1. The equation is odd because of the degree of 3

     2. The leading coefficient is positive 1

     3. Quadrant 3 to quadrant 1

     4. y → -∞, as x → -∞; y → ∞, as x → ∞

• Sketch a graph, given an equation

  1. Determine end behaviours

  2. Factor the equation

  3. Using each factor, determine the zeroes

  4. Substitute 0 for x to find the y-intercept

  5. Plot all solved points, and connect with curved line, and add arrows

     Ex. Sketch y = x³ - 2x³ - 3x

     1. Quadrant 3 to quadrant 1

     2. (x)(x + 1)(x - 3)

     3. x=0 x + 1=0 x - 3=0

        The zeroes are 0, -1, and 3

     4. y = (0)³ - 2(0)³ - 3(0) = 0

        The y-intercept is 0

     

• Describe a set using interval notation

  1. Any value that is a clear, defined point uses [ ]

  2. Any open/infinite points use ( )

     Ex. Describe the parent quadratic function in interval notation

     1. domain: (-∞, ∞) range: [0, ∞]

        1. identify if it is a polynomial question, justify (pg 11)

           1. state the degree and leading coefficient (pg 11)

           2. describing graphs (pg 12)

           3. identifying end behaviours (Pg 12)

           4. graphing (pg 12)

           5. identifying graphs as powers, exponential, periodic, or none

           6. Pg 26 - 1, 2, 3, 5, 6, 8, 10, 11, 12, 13