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