3.6 Warm Up Find the initial point, state the domain & range, and compare to the parent function f(x) = √x. y = 3√x – 1 y = -1/2√x y = - √(x-1) + 2.

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Presentation transcript:

3.6 Warm Up Find the initial point, state the domain & range, and compare to the parent function f(x) = √x. y = 3√x – 1 y = -1/2√x y = - √(x-1) + 2 y = 3√-x

3.6 Graph Rational Functions

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.

a x 1 x EXAMPLE 1 Compare graph of y = with graph of y = 1 –2 x is a The graph of a. b. The graph of y = 3x vertical stretch with a reflection in the x - axis of the graph of vertical shrink of the graph of = y 1 x y = x 1

Compare to parent function: 1. 2. 3.

Steps to graph: Identify and sketch asymptotes. Make a t-chart w/ three points on either side of the vertical asymptote. Plot points & draw graph. Compare to the parent function. Identify domain and range.

Graph y = + k 1 x EXAMPLE 2 Graph y = + 3 and identify its domain and range. Compare the graph with the graph of y = . 1 x

Graph y = 1 x – h EXAMPLE 3 Graph y = and identify its domain and range. Compare the graph with the graph of y = . 1 x– 2 x

Graph y = + k a x – h EXAMPLE 4 Identify the domain and range and compare with the parent function. Graph y = – 3. 2 x + 1

GUIDED PRACTICE for Example 4 Identify the domain and range and compare with the parent function. 5. Graph y = + 6 4 x – 5

GUIDED PRACTICE for Example 4 6. For which function is the domain all real numbers except –3 and the range all real numbers except 7 ? A. y = + 7. 2 x – 3 B. y = – 7. 2 x – 3 C. y = + 7. 2 x + 3 D. y = – 7. 2 x + 3 ANSWER C. y = + 7. 2 x + 3

Determine the asymptotes of the graph of the function. 1. 2.

Write an equation whose graph has the given asymptotes and passes through the given point. x = -2, y = 5; (0, -2)

Write an equation whose graph has the given asymptotes and passes through the given point. 2. x = -4, y = -4; (-5, 3)