Understanding Linear Functions

This video tutorial covers linear functions, including their definition, characteristics, and interpretation. It explains how to determine if a linear function is increasing or decreasing and how to interpret linear models using real-world examples like cab fare calculations. The tutorial also demonstrates how to find a linear function from given points and apply linear functions to solve practical problems, such as calculating savings over time.

What is the general form of a linear function?

• f(x) = mx + b

• f(x) = ax^3 + bx^2 + cx + d

• f(x) = a/x + b

• f(x) = ax^2 + bx + c

If the slope of a linear function is positive, what can we say about the function?

• The function is decreasing.

• The function is increasing.

• The function is quadratic.

• The function is constant.

In the function C(x) = 4 + 2.5x, what does the number 4 represent?

• The total cost for 10 miles.

• The cost per mile.

• The initial cost or flag fee.

• The slope of the function.

How much does the cost increase per mile in the function C(x) = 4 + 2.5x?

• $5.00

• $4.00

• $2.50

• $1.00

Given points (2, -3) and (4, 7), what is the slope of the linear function?

• 2

• 5

• 10

• 3

What is the y-intercept of the linear function determined from points (2, -3) and (4, 7)?

• 5

• 0

• -13

• 13

If you start with $350 and save $90 per month, what is the linear function for total savings?

• S(x) = 90x + 350

• S(x) = 350 - 90x

• S(x) = 90x - 350

• S(x) = 350x + 90

How much will you have saved after 6 months if you save $90 per month starting with $350?

• $350

• $540

• $1,000

• $890

How many months will it take to save at least $1,000 if you save $90 per month starting with $350?

• 6 months

• 7 months

• 9 months

• 8 months

What is the significance of the slope in a savings function like S(x) = 90x + 350?

• It is the total savings after 1 month.

• It represents the initial amount.

• It shows the total savings after 10 months.

• It indicates the monthly savings rate.