Functions

Question 1

What is a mapping?

Answer 1

A mapping takes an input/object and maps it onto an output/image.

Question 2

What is the domain?

Answer 2

range of values that go into the mapping.

Question 3

What is the co domain?

Answer 3

possible values that could come up.

Question 4

What is a many to many mapping?

Answer 4

a value put it could give many different values out and a value out could be given by many different values in.

Question 5

What is a one to many mapping?

Answer 5

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.

Question 6

What is a one to one mapping?

Answer 6

One input will give a unique output.

Question 7

Give an example of a many to many mapping.

Answer 7

y²+x²=1

Question 8

Give an example of a one to many mapping.

Answer 8

f(x)=±√x

Question 9

Give an example of a many to one mapping?

Answer 9

f(x)=x².

Question 10

What mappings are also functions?

Answer 10

one to one and many to one.

Question 11

What is the range?

Answer 11

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.

Question 12

What is a real number?

Answer 12

All numbers, apart from infinity and imaginary ones like the root of a negative number.

Question 13

What does a ε mean?

Answer 13

It is an element of something. e.g. xεℝ means that x is a real number.

Question 14

What does ℝ mean?

Answer 14

the real numbers.

Question 15

What does ℝ^+ mean?

Answer 15

All the real positive numbers.

Question 16

What does ℤ mean?

Answer 16

All the intergers.

Question 17

What does ℚ mean?

Answer 17

All the rational numbers.

Question 18

What does : mean?

Answer 18

such that.

Question 19

What is the way to remember the order for transformations?

Answer 19

y=cf(bx-a)+d. Ignore the f as that is part of y=f(x)

Question 20

What is a transformation of y=f(x-a)?

Answer 20

Move to the right by a.

Question 21

What is a transformation of y=f(x)+b?

Answer 21

Move up by b.

Question 22

What is a transformation of y=af(x)?

Answer 22

stretch by a scale factor of a parallel to the y axis.

Question 23

What is a transformation of y=f(ax)?

Answer 23

stretch the graph by a scale factor of 1÷x parallel to the x axis.

Question 24

What is a transformation of y=-f(x)?

Answer 24

reflect in the x axis.

Question 25

What is a transformation of y=f(-x)?

Answer 25

reflect in the y axis.

Question 26

If you knew the functions of g(x) and f(x), what would the function of gf(x) ?

Answer 26

First you would apply the function of f, then the function of g to that result.

Question 27

How would you find the inverse function of a function?

Answer 27

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.

Question 28

What is an even function?

Answer 28

Line of y=0 is a line of symmetry for the graph of that function.
(-fx)=(fx)

Question 29

What is an odd function?

Answer 29

The graph has rotational symmetry of order two around the origin.
f(-x) = -f(x)

Question 30

What is a periodic function?

Answer 30

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.

Question 31

What is the relationship between the graph of a function the its inverse function?

Answer 31

They will be reflections of each other in the line y=x.

Question 32

What is the modulus function?

Answer 32

The absolute value for something.

│x │is the absolute value of x so you can ignore all any minus signs.

Question 33

How can an inequality such as 2<b?

Answer 33

-b<b><a+b
2=-b+a 8=a+b
Solve simultaneously for a and b</b>

Question 34

How would you solve |x+3|<5 ?

Answer 34

• -5<2

Question 35

What is the range of an inverse of a function?

Answer 35

The domain of the original.

Question 36

Why doesn’t the function f(x)=x² have an inverse?

Answer 36

It is a many to one function so it would become one to many and not be a function.