Function Notation and Real-World Applications

The video tutorial explores mathematical functions, focusing on domain and range. It begins with Sam's problem of downloading songs with a gift card, introducing function notation and evaluating functions. The lesson covers domain and range restrictions, using examples like Molly's earnings problem. It concludes by solving Sam's problem with discounted song prices, emphasizing the importance of understanding functions in real-world scenarios.

How many songs can Sam download if each song costs $2 and he has a $15 gift card?

• 8 songs

• 5 songs

• 6 songs

• 7 songs

If the price of each song is reduced to $1.20, how many songs can Sam download with his $15 gift card?

• 10 songs

• 11 songs

• 13 songs

• 12 songs

What does function notation typically represent?

• A type of graph

• A mathematical equation

• A rule relating domain to range

• A list of numbers

In function notation, what does 'f(x)' represent?

• The range

• The domain

• The constant

• The independent variable

What is the value of f(x) when x is 4 in the function f(x) = 3x - 2?

• 12

• 10

• 14

• 8

Why can't the domain of the function f(x) = 1/x include zero?

• Zero is too small

• Zero is not a real number

• Division by zero is undefined

• Zero is negative

For the function f(x) = √(3x), why can't the domain include negative numbers?

• Negative numbers are not integers

• Negative numbers are too small

• Square roots of negative numbers are undefined

• Negative numbers are not real

How many hours must Molly work to earn $120 if she earns $8 per hour?

• 12 hours

• 15 hours

• 20 hours

• 10 hours

What is the function that represents the money Molly earns based on hours worked?

• f(x) = 8 + x

• f(x) = 8x

• f(x) = 8 - x

• f(x) = x/8

If Sam wants to download songs with a $15 gift card and each song costs $1.20, what is the maximum number of whole songs he can download?

• 13 songs

• 12 songs

• 10 songs

• 11 songs