Functions, Linearity, and Qualitative Graphs

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 does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values increase, the output values decrease.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, defined 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 form a straight line when graphed; it can be represented by equations that are not linear.

Front

What is the difference between continuous and discrete functions?

Back

Continuous functions have outputs for every input in an interval, while discrete functions have outputs only for specific inputs.

Front

What is a qualitative graph?

Back

A qualitative graph represents the general shape and behavior of a function without specific numerical values.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) is paired with exactly one output (y-value).

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 is a slope in the context of linear functions?

Back

The slope of a linear function indicates the steepness of the line and the direction of the relationship between the variables.