Exploring Functions and Function Notation

The video tutorial covers the concept of functions, starting with an introduction to relations and functions. It explains how to identify functions using tables, ordered pairs, and graphs, emphasizing the importance of unique y-values for each x-value. The vertical line test is introduced as a method to determine if a graph represents a function. The tutorial also covers function notation, explaining how to express functions in terms of x and solve related problems.

What is a relation in mathematics?

• An equation with no variables

• A relationship between two quantities

• A graph with intersecting lines

• A function with multiple y-values for each x-value

Which of the following tables represents a function?

• x: 1, 2, 2; y: 3, 4, 5

• x: 6, 6, 7; y: 10, 15, 20

• x: 11, 21, 31; y: 3, 3, 3

• x: 5, 6, 7; y: 10, 15, 20

Which ordered pair set represents a function?

• (-2, -5), (0, 4), (2, 13), (4, 22)

• (10, 10), (12, 10), (14, 12), (16, 12)

• (10, 10), (12, 14), (12, 16), (12, 18)

• (7, 5), (7, 8), (9, 10), (11, 12)

What does the vertical line test determine?

• If a graph is linear

• If a graph is a relation

• If a graph has intersecting lines

• If a graph is a function

Which graph represents a function?

• A graph where a vertical line crosses it twice

• A graph with intersecting lines

• A graph where no vertical line crosses it more than once

• A circular graph

What is the function notation for y = 3x - 2?

• y = f(x) - 2

• f(y) = 3x - 2

• f(x) = 3x - 2

• x = 3y - 2

Evaluate f(5) for the function f(x) = 3x - 2.

• 13

• 15

• 10

• 8

If f(x) = 3x - 2, what is f(-3)?

• -11

• -9

• 7

• 1

Determine x if f(x) = 13 for the function f(x) = 3x - 2.

• 5

• 4

• 3

• 7

Solve for x if f(x) = -18 for the function f(x) = 5x + 7.

• -2

• -4

• -5

• -3