Lesson 3 6 Graph Rational Functions Georgia Performance

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Lesson 3. 6 Graph Rational Functions Georgia Performance Standards: MM 1 A 1 b,

Lesson 3. 6 Graph Rational Functions Georgia Performance Standards: MM 1 A 1 b, MM 1 A 1 c, MM 1 A 1 d

Last week we learned about Odd and Even functions. • Which one is odd

Last week we learned about Odd and Even functions. • Which one is odd and which one is even? Odd Even

Last week we learned about Odd and Even functions. • Which one is odd

Last week we learned about Odd and Even functions. • Which one is odd and which one is even? Odd x -2 h(x) -8 x -2 g(x) 4 -1 -1 -1 1 0 0 1 1 2 8 2 4 Even

Divide 4 by x • Get out a piece of paper and make a

Divide 4 by x • Get out a piece of paper and make a table like this one and fill in all of the values. • Now complete this table and compare the two tables. • Is f(x) odd or even? x 8 f(x) x -8 4 -4 2 -2 1 -1 ½ -½ f(x)

Graph f(x) x -8 f(x) -½ x 8 f(x) ½ -4 -1 4 1

Graph f(x) x -8 f(x) -½ x 8 f(x) ½ -4 -1 4 1 Is f(x) odd or even? 2 2 1 4 Odd ½ 8 -2 -2 -1 -4 -½ -8

Geometer Sketch Pad GSP Rational Function • The blue button at the top will

Geometer Sketch Pad GSP Rational Function • The blue button at the top will start a Geometer’s Sketch Pad drawing that will help us to understand the role of a, h and k in this equation:

What would happen if … • The result would be a zero in the

What would happen if … • The result would be a zero in the denominator. • This is the worst possible thing that can ever happen in your algebraic life. • The line x = h is not a part of the graph of the function. It is the vertical asymptote. • x ≠ h is a restriction on the domain.

What does each part do? • y • The dependent variable. This is the

What does each part do? • y • The dependent variable. This is the • a • x range. • Controls stretch-shrink-flip. • Independent variable this is the domain. • Controls left-right. • h • Controls up-down. • k

What does each part do? a=4 stretch h=3 horizontal shift vertical asymptote x=3 k=1

What does each part do? a=4 stretch h=3 horizontal shift vertical asymptote x=3 k=1 vertical shift horizontal asymptote y=1

Domain and Range • Domain All reals except x ≠ 33 • Range All

Domain and Range • Domain All reals except x ≠ 33 • Range All reals except y≠ ≠ 11

Vocabulary • A rational function has a rule given by a fraction whose numerator

Vocabulary • A rational function has a rule given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0. • An asymptote is a line that a graph approaches more and more closely.

Odd, Even, or Neither? • The parent function was odd. • After the horizontal

Odd, Even, or Neither? • The parent function was odd. • After the horizontal and vertical shift this function is neither.

Range Domain Identify the domain and range. x ≠ -6 x ≠ -3 x≠

Range Domain Identify the domain and range. x ≠ -6 x ≠ -3 x≠ 3 y ≠ -8 y≠ 3 y ≠ -2

Lesson 3. 6 Homework page 153 2, 8, 10, 12, and 14 2. Identify

Lesson 3. 6 Homework page 153 2, 8, 10, 12, and 14 2. Identify the domain and range. 8. Graph y = 1/x and identify the domain and range of the function. 10, 12, 14. Graph and compare to the parent function. 10. 14. 12.