Functions.

Question 1

What is meant by vertical and horizontal in terms of x-axis and y-axis.

Answer 1

• Vertical = y-axis ↑ ↓.
• Horizontal = x-axis → ←.

Question 2

State the type of transformation and change to coordinate pair to the following function notation:
- f(x) - d.

Answer 2

• Function notation: f(x) - d.
• Type of transformation: vertical y-axis translation down d units.
• Change to coordinate pair: (x , y) → (x , y - d).

Question 3

State the type of transformation and change to coordinate pair to the following function notation:
- f(x) + d.

Answer 3

• Function notation: f(x) + d.
• Type of transformation: vertical y-axis translation up d units.
• Change to coordinate pair: (x , y) → (x , y + d).

Question 4

State the type of transformation and change to coordinate pair to the following function notation:
- f(x + c).

Answer 4

• Function notation: f(x + c).
• Type of transformation: horizontal x-axis translation left c units.
• Change to coordinate pair: (x , y) → (x - c , y).

Question 5

State the type of transformation and change to coordinate pair to the following function notation:
- f(x - c).

Answer 5

• Function notation: f(x - c).
• Type of transformation: horizontal x-axis translation right c units.
• Change to coordinate pair: (x , y) → (x + c , y).

Question 6

State the type of transformation and change to coordinate pair to the following function notation:
- -f(x).

Answer 6

• Function notation: -f(x).
• Type of transformation: vertical reflection over x-axis.
• Change to coordinate pair: (x , y) → (x , -y).

Question 7

State the type of transformation and change to coordinate pair to the following function notation:
- f(-x).

Answer 7

• Function notation: f(-x).
• Type of transformation: horizontal reflection over y-axis.
• Change to coordinate pair: (x , y) → (-x , y).

Question 8

State the type of transformation and change to coordinate pair to the following function notation:
- af(x).

Answer 8

• Function notation: af(x).
• Type of transformation: vertical y-axis stretch.
• Change to coordinate pair: (x , y) → (x , ay).

Question 9

State the type of transformation and change to coordinate pair to the following function notation:
- f(bx).

Answer 9

• Function notation: f(bx).
• Type of transformation: horizontal x-axis stretch.
• Change to coordinate pair: (x , y) → (x/b , y).

Question 10

What are the four different relations we can come across in functions?

Answer 10

• one-to-one.
• one-to-many.
• many-to-one.
• many-to-many.

Question 11

What is a one-to-one function relation?

Answer 11

One-to-one means each x value corresponds to one distinct y value.

Question 12

What is a one-to-many function relation?

Answer 12

One-to-many means one x value corresponds to multiple y values.

Question 13

What is a many-to-one function relation?

Answer 13

Many-to-one means multiple x values correspond to the same y value.

Question 14

What is a many-to-many function relation?

Answer 14

Many-to-many means multiple x values correspond to the multiple y values.

Question 15

Out of the four different relations we can come across in functions:

• one-to-one.
• one-to-many.
• many-to-one.
• many-to-many.

Which ones are functions and which ones are not?

Answer 15

Functions are:
- one-to-one.
- one-to-many.

Not functions:
- many-to-one.
- many-to-many.