Constructing Functions

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the ratio of the change in the dependent variable to the change in the independent variable, often represented as 'm' in the slope-intercept form of a line (y = mx + b).

Front

How do you calculate the total cost of a service that includes a flat fee and a variable cost per unit?

Back

To calculate the total cost, use the formula C = flat fee + (variable cost per unit * number of units).

Front

What is a one-time membership fee in the context of a subscription service?

Back

A one-time membership fee is a fixed cost that a customer pays upfront to gain access to a service, in addition to any recurring monthly fees.

Front

How do you set up an equation to represent total expenses based on fixed and variable costs?

Back

Identify the fixed costs and variable costs, then create an equation that sums these costs, typically in the form: Total Expenses = Fixed Costs + (Variable Cost per Unit * Number of Units).

Front

What is the significance of understanding entrance fees in event planning?

Back

Understanding entrance fees helps in budgeting for events, as it allows individuals to calculate the total cost of attending based on additional expenses like tickets or rides.

Front

How do you determine the total number of tickets needed for multiple rides at a carnival?

Back

Multiply the number of rides by the number of tickets required per ride. For example, if each ride costs 3 tickets and you ride 15 times, you need 3 * 15 = 45 tickets.

Front

What is the formula for calculating the total cost of towing a vehicle based on distance?

Back

The total cost of towing can be calculated using the formula C = cost per mile * miles towed + flat fee.

Front

How do you find the initial value in a linear equation?

Back

The initial value in a linear equation is the y-intercept, which is the value of y when x is zero, often represented as 'b' in the slope-intercept form (y = mx + b).

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change and can be expressed in the form y = mx + b.

Front

How can you interpret the slope of a line in a real-world context?

Back

The slope of a line represents the rate of change between two variables, indicating how much one variable changes in response to a change in another variable.