The video tutorial explores Molly's options for a raise at her job, comparing linear and exponential functions. It explains function notation, linear functions, and exponential functions, highlighting common mistakes in evaluating them. The tutorial discusses domain restrictions in real-life contexts, using Molly's raise options as an example. It analyzes both linear and exponential raise options, showing how the domain and range affect Molly's earnings over time. The video concludes that the exponential option is better in the long run.

What are the two raise options Molly can choose from?

• $40 immediately and $5 each month

• $100 immediately and $10 each month

• $200 immediately and 2% each month

• $150 immediately and 1% each month

What does function notation represent?

• A rule relating the domain to the range

• A rule relating the base to the exponent

• A rule relating the range to the domain

• A rule relating the slope to the intercept

What is the slope of the linear function f(x) = 3x - 2?

• 3

• 4

• 2

• 5

What is a key characteristic of exponential functions?

• They have a linear growth

• They have a constant rate of change

• They have a variable base

• They have a constant base raised to a variable power

What mistake is commonly made when evaluating exponential functions?

• Multiplying before simplifying exponents

• Subtracting before dividing

• Dividing before adding

• Adding before multiplying

What can cause a function to have a restricted domain?

• Values that make the function constant

• Values that make the function linear

• Values that make the function exponential

• Values that make the function undefined

In the context of Molly's raise, what restricts the domain of the function?

• The amount of money she earns

• The percentage increase each month

• The number of years she plans to work

• The initial amount she receives

What is the function for Molly's linear raise option?

• f(x) = 50 + 10x

• f(x) = 100 + 2x

• f(x) = 150 + 1.01x

• f(x) = 40 + 5x

Which raise option is better for Molly over a long period?

• Neither is beneficial

• Both are equal

• The exponential option

• The linear option

At what point does the exponential function exceed the linear function in Molly's raise options?

• At 85 months

• At 30 months

• At 96 months

• At 50 months