Non-permissible Values
Vertical Asymptotes
Horizontal Asymptotes
Points of Discontinuity
X and Y-intercepts
Rational Functions
Miscellaneous
200
For rational functions, division by what number creates non-permissible values?
Zero
200
Vertical Asymptotes occur when uncancelled terms in the denominator lead to division by what number?
zero
200
When does a rational function have a Horizontal Asymptote? (name BOTH cases)
Degree of numerator < degree of denominator
OR
Degree of numerator = degree of denominator
200
When can a rational function have a Point of Discontinuity?
When a factor in the numerator cancels with a factor in the denominator.
200
What is the y-intercept of
y=(x^3-2x+8)/(4x^2-x-4)
(0,-2)
200
Of "domain", "range", or "both", what is affected by Points of Discontinuity?
BOTH domain and range
200
Where did Mr. Estrada go for his winter holiday?
Guatemala
400
What is the non-permissible value in the expression
5/(x-2)
x=2
400
What is the equation of the VA in the function
y=1/(x+4)
x=-4
400
What is the HA of the function
y=-2/x
y=0
400
The PoD of the function y=(x+2)/((x+2)(x+3)) has what x-coordinate?
-2
400
What is the x-intercept of
y=(x-5)/(2x+3)
(5,0)
400
As x-values of a rational function get close to its non-permissible values near VA, what happens to the y-values?
They approach either
infty or -infty
400
What is Mr. Nara's favourite movie?
Back to the Future
600
What is the non-permissible value(s) in the expression (x+2)/(x^2+5x+6)
x=-2, x=-3
600
What are the equation(s) of all VA(s) in the function
y=(-2(x+1)(x-2))/((x+1)(x+8))
x=-8
600
What is the HA of the function
y=(5x^3-12x^2+7x-6)/(2x^3+x^2-13x+11)
y=5/2
600
What are the coordinates (x,y) of the PoD of y=(x^2+x-20)/(x+5)
(-5,-9)
600
What is the x-intercept of
y=(x^2+5x+6)/(x+2
(-3,0)
600
What is the equation of the function below?
y=(x+2)/((x+3)(x-2)
600
How old will Ms. Lees turn this year?
30!!!
800
Name one of the two types of discontinuities which result from a non-permissible value in a rational function
Vertical Asymptotes or Points of Discontinuity
800
What are the equations of all VA in the function
y=(2x+1)/(4x^3+13x^2+3x)
x=0,x=-1/4,x=-3
800
What is the HA of the function
y=(-3)/(x+5)+2
y=2
800
What are the coordinates (x,y) of the PoD of
y=(x-3)^2/(x-3)
(3,0)
800
What is the x-intercept of
y=2/(x+4)-1
(-2,0)
800
What is the range of the function
y=(5x(x-3))/(x-3
y\ne15, yinR
800
Which scientist is Mr. Magi's profile picture? *HINT* He's the "most handsome scientist" of all time.
Amedeo Avogadro
1000
What are the non-permissible value(s) of the function y=(x^2-1)/(x^2+1)
No non-permissible values
1000
What is the equation of the VA in the function
y=(x-1)/(x^3+1)
x=-1
1000
When the degree of the numerator is ONE GREATER than the degree of its denominator, it will NOT have a HA, but instead has what?
Oblique Asymptote
1000
What are the coordinates (x,y) of the PoD of
y=(x-3)/(x-3)^2
It doesn't have one!
1000
What is the x-intercept of
y=x/x^2
It doesn't have one!
1000
Rewrite the equation of the function y=(3x-2)/(x+1) in the form y=a/(x-h)+k
y=-5/(x+1)+3
1000
What is the name of Mr. Bellamy's son? *HINT* It's also the name of a famous mathematician known for a triangle.
Pascal
