Linear vs Nonlinear Functions

Front

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

How can you tell if a relation is not a function?

Back

If any x-value is paired with more than one y-value.

Front

What does it mean for a function to be linear?

Back

A function is linear if its graph forms a straight line, indicating a constant rate of change.

Front

What does it mean for a function to be nonlinear?

Back

A function is nonlinear if its graph does not form a straight line, indicating a variable rate of change.

Front

Give an example of a linear function.

Back

y = 2x + 3 is a linear function.

Front

Give an example of a nonlinear function.

Back

y = x^2 is a nonlinear function.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

Front

What is a table of values in relation to functions?

Back

A table that shows pairs of x-values and their corresponding y-values.

Front

What does it mean if an x-value is repeated in a table of values?

Back

If an x-value is repeated with different y-values, the relation is not a function.

Front

What is the slope of a linear function?

Back

The slope is the rate of change of y with respect to x, indicating how steep the line is.