Comparing, Describing, & Constructing Functions

Front

What is the equation for the total cost (C) of towing a vehicle for m miles if the service center charges a flat fee of $50 plus $8 per mile?

Back

C = 8m + 50

Front

How do you express the relationship between the number of weeks (x) and the number of pieces learned (y) if Ryan starts with 7 pieces and learns 2 new pieces each week?

Back

y = 2x + 7

Front

If Nate’s service is described by the equation y = 4x + 6, what is the cost for 8 movies?

Back

$38

Front

What does the slope of a linear function represent in a real-world context?

Back

The slope represents the rate of change, indicating how much the dependent variable changes for a unit change in the independent variable.

Front

If Quick Cabs charges according to the function C(m) = 0.55m + 3.75, what does the 0.55 represent?

Back

The cost per mile.

Front

What is the fixed fee in the function C(m) = 0.55m + 3.75?

Back

$3.75

Front

How do you determine which service is cheaper when comparing two linear functions?

Back

Evaluate both functions at the same input value and compare the outputs.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept represents the value of the dependent variable when the independent variable is zero.

Front

If a function has a slope of 3, what does this indicate about the relationship between the variables?

Back

For every 1 unit increase in the independent variable, the dependent variable increases by 3 units.

Front

What is the general form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.