Understanding Functions and Their 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 is a linear function?

Back

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Examples include quadratic functions, exponential functions, and trigonometric functions.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if it forms a straight line. The slope remains constant throughout the graph.

Front

What is slope-intercept form?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function; it indicates how much the output value (y) changes for a unit change in the input value (x).

Front

What is the y-intercept?

Back

Front

What is the vertical line test?

Back

The vertical line test is a method used 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 table of values?

Back

A table of values is a way to organize input-output pairs for a function, showing how each input corresponds to an output.

Front

How do you determine if a table represents a linear function?

Back

To determine if a table represents a linear function, check if the differences between consecutive output values are constant when the input values increase by the same amount.