Comparing Functions

Front

What is the equation to calculate total cost when there is a fixed fee and a variable fee per hour?

Back

y = mx + b, where m is the variable cost per hour, b is the fixed fee, and y is the total cost.

Front

Define 'rate of change' in the context of functions.

Back

The rate of change is the ratio of the change in the output value (y) to the change in the input value (x), often represented as slope (m) in linear functions.

Front

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

Back

The slope represents the rate at which one quantity changes in relation to another, such as cost per hour or speed.

Front

How do you determine which function has the greatest initial fee?

Back

Compare the y-intercepts of the functions; the function with the highest y-intercept has the greatest initial fee.

Front

What is the formula for the total cost of x pounds of fruit if there is a fixed charge and a variable charge per pound?

Back

y = px + b, where p is the cost per pound, b is the fixed charge, and y is the total cost.

Front

If a function is represented as y = 2.50x + 3, what does 2.50 represent?

Back

2.50 represents the variable cost per pound of fruit.

Front

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

Back

The y-intercept represents the fixed cost incurred before any variable costs are added.

Front

How can you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does it mean if two functions have the same rate of change?

Back

It means they increase or decrease at the same rate, resulting in parallel lines when graphed.

Front

What is the equation for a linear function that represents a business charging a flat fee plus a variable fee?

Back

y = mx + b, where m is the variable fee per unit and b is the flat fee.