EQ: How does dividing by zero affect the graph of a function?

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Presentation transcript:

EQ: How does dividing by zero affect the graph of a function? Holes & asymptotes EQ: How does dividing by zero affect the graph of a function?

Think about it… A group of people rent a bus for a day. The total cost of the bus is shared equally among the passengers. x = the number of passengers. y = the cost for each passenger in dollars.

Rational Functions The quotient of two polynomials

Review: Parent Function

Describe the transformations 1. 2. 3.

Graphing in the calculator When entering a rational function into the calculator be sure to put parentheses around the entire numerator and entire denominator f(x) =

Graph: Window → “Xmin = 1.5” “Xmax = 2.5”

Points of discontinuity (breaks in the graph) occur at values where the DENOMINATOR = 0 Example: x cannot equal -1 because… x + 1 = (-1) + 1 = 0

HOLES X-values where the denominator = 0 and the factors cancel out Ex.)

Vertical Asymptotes X-values where the denominator = zero and the factors do not cancel out. Ex 1)

Finding holes & asymptotes Method 1: Factor, set denominator equal to zero and solve. Method 2: Use the table to find the “error”. Method 3: Identify transformations

Method 1: Factor, Solve

Method 2: table

Method 3: transformations

1. Hole(s): Asymptotes: Domain:

2. Hole(s): Asymptotes: Domain:

3. Hole(s): Asymptotes: Domain:

4. Hole(s): Asymptotes: Domain:

5. Hole(s): Asymptotes: Domain:

6. Hole(s): Asymptotes: Domain:

7. Hole(s): Asymptotes: Domain:

Write a rational function that has.. A point of discontinuity (hole) at x=3 and a vertical asymptote at x=-2

Write a rational function that has.. A point of discontinuity at and a vertical asymptote at x=-6

Write a rational function that has.. A point of discontinuity at x=- 1 and x=4 and a vertical asymptote at x=2

Write a rational function that has.. A point of discontinuity at x=8 and a vertical asymptote at x=-2 and x=3

Write a rational function that has.. No points of discontinuity and a vertical asymptote at x=4 and x=-5

Exit ticket Make up a function that has both a hole & an asymptote. Identify their locations.