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Rational Functions
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What are x = -3 and x = 4
The vertical asymptotes
The holes
My favorite numbers
The x-intercepts
Oops!
Okay!
Holes occur when the value of a rational function is...
0
1/0
0/0
x/0
Oops!
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When the numerator's degree is bigger, the Horizontal Asymptote is...
x = 0
There is none
y = 0
Infinity
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The horizontal asymptote will be equal to the ratio of its leading coefficients when
the degree on the top is bigger
98 Degrees was a great band
the degree on the bottom is bigger
when the degrees are the same
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Find the Horizontal Asymptote
x = 0
y = 0
x = -2
y = -2
Oops!
Okay!
Vertical Asymptotes are always written in the form...
y = mx + b
y = #
Chuck Norris
x = #
Oops!
Okay!
What are the x-intercepts of the following function?
x = 4, -4
There are none
x = 0, 4, -4
x = 0, 16
Oops!
Okay!
Where is the y-intercept in the following function?
y = 1/4
There's a hole there
Witness protection
0
Oops!
Okay!
Horizontal Asymptotes are always written in the form....
Horizontal whaa?
y = #
x = #
Take the L.
Oops!
Okay!
What is the Horizontal Asymptote of the function
There is none
y = 0
y = -1/3
x = 0
Oops!
Okay!
What is the domain of this function?
All reals except x = -4, 1
All real numbers
All reals except x = 1, -1
x = 1, -1
Oops!
Okay!
Where are the holes in the following function?
There are none
Swiss Cheese
x = 4, -4
At the origin
Oops!
Okay!
Setting the numerator equal to zero and solving will help you find...
Y-intercepts
X-Intercepts
Purpose in life
Excluded Values
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If the denominator's degree is bigger than the numerator's degree, Horizontal Asymptote is...
x = 0
y = 1
y = 0
There is none
Oops!
Okay!
Find the holes (if any) in the following function...
There are none
x = 4
x = 2, -1
x = -2, 1
Oops!
Okay!
Where are the x-intercepts in the following graph...
x = 2
x = -2
x = 4
x = -2/3
Oops!
Okay!
Evaluating a rational function at zero is the best way to determine where...
to go for fresh produce
the x-intercepts are
the holes are
the y-intercept is
Oops!
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Setting the denominator equal to zero and solving will help you find...
Holes and Vertical Asymptotes
Vertical Asymptotes
Horizontal Asymptotes
Holes
Oops!
Okay!
Where is the vertical asymptote of this function?
x = -1
x = 1, -1
x = 1
x = 4, -1
Oops!
Okay!
Describe the domain of the following function...
All reals except x = -2, 3
All reals except x = -3, 2
All reals except x = -5, 1
All reals except x = -1, 5
Oops!
Okay!
Find the Horizontal Asymptote of this function...
There is none
y = 1/4
y = -1/4
x = -1/4
Oops!
Okay!
Where is the y-intercept of the following graph?
There's a hole there
There's an asymptote there
At the origin
On the beach in Tahiti sipping a margarita
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Okay!
Where is the y-intercept of this function?
y = -8
x = 8
y = 8
x = -8
Oops!
Okay!
Excluded values resulting from factors that can NOT be canceled will cause...
Horizontal Asymptotes
Tsunamis in 3rd World countries
Holes
Vertical Asymptotes
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Where is/are the x-intercept(s) of this function?
x = 4
x = -1, 4
y = 8
x = -1
Oops!
Okay!
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