Representing Functions; Linear vs Nonlinear Functions

Front

What is a function?

Back

A function is a relationship between two sets of values where each input (independent variable) has exactly one output (dependent variable).

Front

What is the independent variable in a function?

Back

The independent variable is the input of the function, often represented by 'x', which determines the value of the dependent variable.

Front

What is the dependent variable in a function?

Back

The dependent variable is the output of the function, often represented by 'y', which depends on the value of the independent variable.

Front

Write an equation to represent the function: Jesse is traveling at a constant speed of 80 kilometers per hour. The distance, d kilometers, he travels is a function of the amount of time, t hours, that he takes.

Back

d = 80t

Front

Write an equation to represent the function: Mr. Cooper pays a monthly charge of $40 for a family cell phone plan. Each additional family member pays $10 every month. The total amount of money, y dollars, Mr. Cooper and his family members pay each month is a function of the number of additional family members, x.

Back

y = 10x + 40

Front

Write an equation to represent the function: Sofia has $60 on her bus pass initially. Every time she rides a bus, $1.50 is deducted from the value on her pass. The amount of money, y dollars, she has on her pass is a function of the number of times, x, that she rides a bus.

Back

y = 60 - 1.5x

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line, meaning the rate of change is not constant.

Front

What is the slope of a linear function?

Back

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

Front

How do you find the rate of change in a linear function?

Back

The rate of change can be found by calculating the change in the dependent variable divided by the change in the independent variable (rise/run).