Functions

Question 1

What is a mapping?

Answer 1

A mapping is any rule connecting input values (objects) and output values (images).

Question 2

What types of mappings exist?

Answer 2

Mappings can be many-to-one, one-to-many, one-to-one, or many-to-many.

Question 3

What is a function?

Answer 3

A many-to-one or one-to-one mapping is called a function.

Question 4

What is the domain of a mapping or function?

Answer 4

The domain is the set of possible input values (values of x).

Question 5

What is the range of a mapping or function?

Answer 5

The range is the set of output values.

Question 6

What does the transformation f(x) → f(x-t) + s represent?

Answer 6

It represents a translation column vector (t s)

Question 7

What does the transformation f(x) → af(x) represent?

Answer 7

It represents a one-way stretch, parallel to the y-axis, with scale factor a.

Question 8

What does the transformation f(x) → f(ax) represent?

Answer 8

It represents a one-way stretch, parallel to the x-axis, with scale factor a.

Question 9

What does the transformation f(x) → -f(x) represent?

Answer 9

It represents a reflection in the x-axis.

Question 10

What does the transformation f(x) → f(-x) represent?

Answer 10

It represents a reflection in the y-axis.

Question 11

What is a composite function?

Answer 11

A composite function is obtained when one function (g) is applied to the output from another function (f).

Question 12

What is the notation for composite functions?

Answer 12

The notation used is g(f(x)) or gf(x).

Question 13

What is an inverse function?

Answer 13

For any one-to-one function f(x), there is an inverse function f^(-1)(x).

Question 14

How are the curves of a function and its inverse related?

Answer 14

The curves are reflections of each other in the line y = x.

Question 15

What does the modulus of x mean?

Answer 15

The modulus of x, written |x|, means the positive value of x.

Question 16

What is the definition of the modulus function?

Answer 16

The modulus function is defined as:
1 for x > 0
0 for x = 0
-x for x < 0.

Question 17

How is the modulus function sketched?

Answer 17

Any part of the graph of the function that is below the x-axis is reflected in the x-axis.