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 a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form 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 and can include curves, parabolas, and other shapes.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

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

Back

A graph represents a function if every x-value (input) has exactly one corresponding y-value (output).

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change, meaning the difference in y-values divided by the difference in x-values is the same for all intervals.

Front

What is the slope of a line?

Back

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

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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.