Characteristics of Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, and 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 line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is a positive domain in a function?

Back

A positive domain means that the function only accepts positive input values (x > 0).

Front

How do you identify a linear function from a graph?

Back

A linear function can be identified by its straight-line graph, which has a constant slope.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, b) in the equation f(x) = mx + b.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to have a slope of 1/2?

Back

A slope of 1/2 means that for every 2 units you move horizontally to the right, the function moves up 1 unit.