Functions Flashcards
What is a mapping?
A mapping takes an input/object and maps it onto an output/image.
What is the domain?
range of values that go into the mapping.
What is the co domain?
possible values that could come up.
What is a many to many mapping?
a value put it could give many different values out and a value out could be given by many different values in.
What is a one to many mapping?
A single value in the co domain will be given by a single value in the domain, but a single value in the domain could give many different values in the co domain.
What is a one to one mapping?
One input will give a unique output.
Give an example of a many to many mapping.
y²+x²=1
Give an example of a one to many mapping.
f(x)=±√x
Give an example of a many to one mapping?
f(x)=x².
What mappings are also functions?
one to one and many to one.
What is the range?
Actual values that come up in the co-domain.
e.g. the domain could be a list of children and the co-domain could pets they have. However, not all the possible pets like lizard and fish are chosen, but they are still part of the co-domain. Things like dogs and cats that do come up are part of the range.
What is a real number?
All numbers, apart from infinity and imaginary ones like the root of a negative number.
What does a ε mean?
It is an element of something. e.g. xεℝ means that x is a real number.
What does ℝ mean?
the real numbers.
What does ℝ^+ mean?
All the real positive numbers.
What does ℤ mean?
All the intergers.
What does ℚ mean?
All the rational numbers.
What does : mean?
such that.
What is the way to remember the order for transformations?
y=cf(bx-a)+d. Ignore the f as that is part of y=f(x)
What is a transformation of y=f(x-a)?
Move to the right by a.
What is a transformation of y=f(x)+b?
Move up by b.
What is a transformation of y=af(x)?
stretch by a scale factor of a parallel to the y axis.
What is a transformation of y=f(ax)?
stretch the graph by a scale factor of 1÷x parallel to the x axis.
What is a transformation of y=-f(x)?
reflect in the x axis.