Sets
In your own words, describe what a set is.
A set is a collection of distinct objects such as numbers, letters, symbols etc..
Explain why they are named rational equations.
They contain rational expressions (numerator/denominator) similar to how a rational number is a fraction of two intergers.
When we have two different equations plotted on a graph and we are looking for the solution of the equations what point are we interested in?
The intersection of the two graphs
Name the 3 types of reflections and how to identify each one.
x axis -> y = -f(x)
y axis -> y = f(-x)
y = x -> x = f(y)
If (A n B) = 0, what can we say about the sets A and B?
A and B are disjoint sets
What are non-permissible values? Why do they occur?
They occur because we cannot divide by 0. Therefore we must be careful what values of our variable we pick.
Name 5 base graphs we have studied and describe the base shape of each graph.
y = x
y = x^2
y = x^3
y = 1/x
y = 2^x
In what order should you apply transformations?
Stretches
Reflections
Translations
What does (A u B)' mean? What area does this represent in a Venn Diagram.
The compliment of A or B
In the Venn Diagram, everything except A or B
What happens to the graph of a rational equation when we are able to cancel out a variable term in the numerator/denominator?
A point of discontinuity forms.
If I have a quadratic function with roots at a and b. What is the equation of the line of symmetry of this quadratic function?
Roots are at a and b. Line of symmetry will be in the middle of a and b. So the line of symmetry will be at x = (a+b)/2
State what each parameter in the general form of a transformation represents.
a
b
h
k
a - vs stretch by a and if a < 0 reflection on x axis
b - hs stretch by 1/b and if b < 0 reflection on x axis
h - ht by h units
k - vs by k units
Given two sets A and B. A and B have common elements. What is the value of (A n B) n (A n B')?
0
Simplify the following rational expression and state any NPVs.
(x+2)/(x-3) where x cannot equal -3, -1/2, 3, 4
Is a scenario possible where two functions can have 3 solutions? If so provide an example.
Yes
ex:
y = (1/3)x^3
y = x
Name a function that when reflected along the line y=x has no change in its shape.
y = 1/x
Given
e = {x: 0 < x < 11}
A = {x: x are even numbers}
If it is possible, create a set B so that n(A n B) = n(e).
It is not possible, A n B can only have a maximum possible number of intersections of 5.
Solve the following rational equation. State any NPVs.
x = -3
slope = 0
If we have a parabola, and we know the coordinate where the slope is found to be 0 we can say that point can be the minimum/maximum point.
Ex: Trajectory of a ball, we can have the exact point where it is at it's maximum height
The point (2, 4) lies on our parent function y=f(x). The function is transformed and now has become (-3, 9). What is a possible combination of transformations that the parent function has experienced if the function experience at least 1 stretch.
ex:
vs by 2
vt up 1
ht 1 right
reflection on the y axis