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