Functions Word Problems

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a graph, or a table.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you write an equation for a situation involving a flat fee and a variable cost?

Back

The equation is written as C = fixed fee + (variable cost per unit * number of units).

Front

If a runner's speed is constant, how can you express the distance covered over time?

Back

Distance can be expressed as D = rt, where D is distance, r is rate (speed), and t is time.

Front

What does the slope of a line represent in a linear function?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

How do you determine the total cost from a babysitting scenario?

Back

Total cost C can be calculated using the equation C = 5h + 3, where h is the number of hours babysat.

Front

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

Back

The y-intercept is the value of y when x is 0; it represents the starting point of the function.

Front

How can you express a situation where a man descends from a height?

Back

The height can be expressed as y = 100 - 30x, where y is the height after x minutes.

Front

What is a real-world example of a linear function?

Back

An example is the cost of renting a car, which can be modeled as y = 0.75x + 35, where x is miles driven.

Front

How do you interpret the coefficients in a linear equation?

Back

Coefficients represent the rate of change; for example, in C = 5h + 3, 5 is the cost per hour.