Analyzing the Domain of Linear Functions in Real Life Word Problems

The video tutorial explores Emily's options for purchasing music online, comparing the costs of downloading songs individually versus using an online program. It introduces function notation and explains how to graph linear functions, highlighting common misunderstandings. The tutorial emphasizes the importance of understanding domain restrictions in real-life contexts, using Emily's purchase scenario as an example. It concludes by comparing the costs of different purchase options, demonstrating how domain restrictions affect decision-making.

What are the two options Emily has for purchasing music online?

• Download songs for $2.00 each or pay $10 for a program and $1.50 per song

• Rent songs for $1 each or buy them for $2 each

• Buy a CD for $15 or stream music for free

• Purchase a subscription for $5 per month or buy songs for $3 each

What does the function notation y = F(X) represent?

• A rule that relates the X-axis to the Y-axis

• A rule that relates the slope to the intercept

• A rule that relates the domain to the range

• A rule that relates the range to the domain

What is the slope of the linear function F(X) = 3X - 2?

• 1.5

• 6

• 3

• 2

Why might a function have a restricted domain in real-life situations?

• Because the function is always linear

• Because some values of X make the function undefined

• Because all values of X are always valid

• Because the range is always restricted

In the context of Emily's music purchase, what restricts the domain of the function F(X) = 2X?

• The number of songs is unlimited

• The number of songs can be negative

• The number of songs must be a whole number

• The number of songs can be fractional

What is the maximum number of songs Emily can purchase if each costs $2 and she has $40?

• 20

• 15

• 25

• 10

Which option becomes more cost-effective if Emily has more than $40 to spend?

• Buying songs for $2 each

• Using the online program and paying $1.50 per song

• Buying a subscription for $5 per month

• Renting songs for $1 each