Identifying Functions

Front

What is a function?

Back

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

Front

What is a nonlinear function?

Back

A nonlinear function is a function whose graph is not a straight line; it can be a curve.

Front

What does the graph of a linear function look like?

Back

The graph of a linear function is a straight line.

Front

What is the equation of a linear function?

Back

The equation of a linear function can be represented as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the definition of a constant rate of change?

Back

A constant rate of change means that for every unit increase in x, y increases by a fixed amount.

Front

What is an example of a nonlinear equation?

Back

An example of a nonlinear equation is y = x^3 - 3x + 1.

Front

How can you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no two pairs have the same x-value.

Front

What ordered pair can be added to the set {(5, 7), (6, 8), (7, 9)} to keep it a function?

Back

The ordered pair (8, 10) can be added to keep it a function.

Front

What does it mean if a graph fails the vertical line test?

Back

If a graph fails the vertical line test, it means that there are multiple y-values for at least one x-value, indicating it is not a function.

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.