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.
What is a transformation of y=f(-x)?
reflect in the y axis.
If you knew the functions of g(x) and f(x), what would the function of gf(x) ?
First you would apply the function of f, then the function of g to that result.
How would you find the inverse function of a function?
Think of it as an equation where y is the subject. You would rearrange so that x was the subject and was given in terms of y.
What is an even function?
Line of y=0 is a line of symmetry for the graph of that function.
(-fx)=(fx)
What is an odd function?
The graph has rotational symmetry of order two around the origin.
f(-x) = -f(x)
What is a periodic function?
The graph has a repeating pattern.
i.e. if there is a value of k for which f(x + k) = f(x) for all x.
The smallest possible value of k is the period of the function.
What is the relationship between the graph of a function the its inverse function?
They will be reflections of each other in the line y=x.
What is the modulus function?
The absolute value for something.
│x │is the absolute value of x so you can ignore all any minus signs.
How can an inequality such as 2<b?
-b<b><a+b
2=-b+a 8=a+b
Solve simultaneously for a and b</b>
How would you solve |x+3|<5 ?
- -5<2
What is the range of an inverse of a function?
The domain of the original.
Why doesn’t the function f(x)=x² have an inverse?
It is a many to one function so it would become one to many and not be a function.
