Exploring Functions in Unit 7-2

This video tutorial covers the concept of functions, explaining their characteristics and how to determine if a relation is a function. It introduces function notation and provides real-life examples, such as a vending machine analogy. The tutorial also explains the vertical line test for identifying functions on a graph. In the second part, it focuses on evaluating functions with given values, using examples to demonstrate the process.

What is a function in mathematical terms?

• A relation where each element of the range is paired with exactly one element of the domain.

• A relation where each element of the domain is paired with exactly one element of the range.

• A relation where elements of the range can be paired with multiple elements of the domain.

• A relation where elements of the domain can be paired with multiple elements of the range.

In the vending machine example, what happens if you press the button labeled 'W'?

• You get a bottle of Gatorade.

• You get a bottle of Pepsi.

• You get a bottle of orange soda.

• You get a bottle of water.

How do you read the function notation f(x)?

• f divided by x

• f times x

• f of x

• f plus x

What is the input in the function notation f(x)?

• f

• x

• y

• f(x)

Which of the following is true for a relation to be a function?

• None of the x-values can repeat.

• Both x and y values can repeat.

• Only y-values can repeat.

• None of the y-values can repeat.

What does the vertical line test determine?

• If a graph is a function.

• If a graph is linear.

• If a graph is quadratic.

• If a graph is continuous.

In the vertical line test, what indicates that a graph is not a function?

• The vertical line touches the graph at only one point.

• The vertical line does not touch the graph.

• The vertical line touches the graph at exactly two points.

• The vertical line touches the graph at more than one point.

What is the value of f(3) if the function is defined as f(x) = 3x - 2?

• 9

• 5

• 7

• 11

What is the value of f(-2) if the function is defined as f(x) = 3x - 2?

• -4

• -10

• -6

• -8

If h(z) = z^2 - 4z + 9, what is h(-3)?

• 45

• 27

• 33

• 39