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