warmup alg 2 6 mar 2012
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Warmup Alg 2 6 Mar 2012. Warmup Alg 2 7 & 8 Mar 2012. Warmup Alg 2 9 Mar 2012. Agenda. Don't forget about resources on mrwaddell.net Chapter 8: Rational Functions Can you graph simple rational functions?. Section 8.2: Simple Rational Functions and their graphs. Vocabulary. - PowerPoint PPT PresentationTRANSCRIPT
Warmup Alg 2 6 Mar 2012
Warmup Alg 2 7 & 8 Mar 2012
Warmup Alg 2 9 Mar 2012
Agenda• Don't forget about resources on
mrwaddell.net
• Chapter 8: Rational Functions• Can you graph simple rational functions?
Section 8.2: Simple Rational Functions and
their graphs
Vocabulary
Domain
Range
The places along the x axis where the graph lives
The places along the y axis where the graph lives
Vocabulary
Rational Expression
Asymptote
Vertical
Horizontal
A quotient of 2 polynomials
An invisible line that the graph gets close to, but never touches.
Vocabulary
Vertical Asymptote Occurs anywhere the fraction is divided by zero.
You must, MUST, MUST check to find out where the denominator equals zero.
This is NOT optional.
Checking for Vertical Asymptotes
xx662 3 Is this a Rational function?
Yes, the numerator is cubic, the denominator is linear
Where does the denominator equal zero?6x Take the bottom= 0
Set it equal to zero and solve.
x = 0
There is a vertical asymptote at x = 0
Checking for Vertical Asymptotes
732285
2
23
xxxx x
Is this a Rational function?
No, the 2x messes it up!
Finding the domain
12662 3
xx What is the domain of the
expression?
Where does the denominator equal zero?
6x -12 Take the bottom= 0Set it equal to zero and solve.
6x = 12
There is a vertical asymptote at x = 2 x = 2
The domain is: All Reals except x = 2
Graphing Simple Rational Functions
xy 1 The parent function for all
rationals.
Where does the denominator equal zero?
x Take the bottom= 0Set it equal to zero and solve.
There is a vertical asymptote at x = 0
The domain is: All Reals except x = 0
xy 1
x= 0 is the vertical asymptote, and y=0 is the horizontal asymptote
The domain is all reals and x ≠ 0
The range is all reals and y ≠ 0
Textbook notes
xy 6
x= 0 is the vertical asymptote and y =0 is the horizontal asymptote.
The domain is all reals except x = 0
The range is all reals except y = 0
xy 12
x= 0 is the vertical asymptote and y = 0 is the horizontal asymptote.
The domain is all reals except x = 0
The range is all reals except y = 0
xy 4
x= 0 is the vertical asymptote and y = 0 is the horizontal asymptote.
The domain is all reals except x = 0
The range is all reals except x = 0
Graphing Simple Rational Functions
xay What does the “a” do to the
equation?
How did the graphs change as “a” went from 1 to 12?
Just like all the other translations, “a” makes it skinny or fat, and a negative “flipped it” around the X AXIS.
Graphing Simple Rational Functions
khxay
What do you think the “h” and the “k” do to the graph?
If you said, “The same thing as with radicals and quadratics and polynomials,” you are RIGHT!
“h” moves it left and right, (but opposite to the sign” and “k” moves it up and down!
Textbook notes
32
x
y
x= -3 is the vertical asymptote and y = 0 is the horizontal asymptote.
The domain is all reals except x = -3
The range is all reals except x = 0
432
x
y
x= -3 is the vertical asymptote and y = 4 is the horizontal asymptote.
The domain is all reals except x = -3
The range is all reals except x = 4
Graphing Rational Functions
dcxbaxy
Now they are a little more complex.
The numerator and denominator are both lines, that is very important.
The vertical asymptote is at x = -d/c
The horizontal asymptote is at y = a/c
432
xxy
x = 4 is the vertical asymptotey=2 is the horizontal asymptote.
The domain is all reals except x = 4
The range is all reals except y = 2/1 = 2
Textbook notes
Assignment
Section 8.2: 11 – 18, 29 – 34