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3.6 Warm UpFind the initial point, state the
domain & range, and compare to the parent function f(x) = √x.
1. y = 3√x – 1
2. y = -1/2√x
3. y = - √(x-1) + 2
4. 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.
EXAMPLE 1 Compare graph of y = with graph of y = ax
1x
b. The graph of1
y = 3xvertical stretch with a reflection in the x - axis of the graph of
vertical shrink of the graph of
=y1x y = x
1
–2x is aThe graph ofa.
Compare to parent function:
1.
2.
3.
6y
x
1
6y
x
3
2y
x
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.
EXAMPLE 2
Graph y = + 3 and identify its domain and range. Compare the graph with the graph of y = .
1x 1
x
Graph y = + k1x
EXAMPLE 3
Graph y = and identify its domain and range.
Compare the graph with the graph of y = .
1x– 2
1x
Graph y = 1
x – h
EXAMPLE 4 Graph y = + k ax – h
Graph y = – 3. 2
x + 1Identify the domain and range and compare with the parent function.
GUIDED PRACTICE for Example 4
5. Graph y = + 6 4x – 5
Identify the domain and range and compare with the parent function.
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 = + 7.2x – 3 B. y = – 7.2
x – 3
C. y = + 7.2x + 3 D. y = – 7.2
x + 3
ANSWER
C. y = + 7.2x + 3
Determine the asymptotes of the graph of the function.
1.
2.
714
5y
x
103
5 5y
x
Write an equation whose graph has the given asymptotes and passes through the given point.
1. 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)
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