Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation f(x) = mx + b.

Front

How do you determine if a function is linear or nonlinear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b. If it cannot be expressed in this form or if its graph is not a straight line, it is nonlinear.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the domain?

Back

The domain is {-4, 0, 1, 2}.

Front

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the range?

Back

The range is {-4, -3, 1}.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every x-value has exactly one corresponding y-value. This is known as the vertical line test.

Front

What is an example of a real-world situation that can be modeled by a linear function?

Back

Sonia has $40 in her lunch account and pays $2 each day to eat lunch. This situation can be modeled by the linear function f(x) = 40 - 2x, where x is the number of days.