Understanding Functions and Their Graphs

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a table, or a graph.

Front

What is a linear function?

Back

Front

What is a nonlinear function?

Back

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

Front

How can you determine if a function is linear or nonlinear from a table of values?

Back

If the differences between consecutive outputs (y-values) are constant for equal differences in inputs (x-values), the function is linear. If not, it is nonlinear.

Front

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

Back

A graph represents a function if every vertical line intersects the graph at most once. This is known as the vertical line test.

Front

What is the vertical line test?

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The vertical line test is 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

Give an example of a linear function.

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Front

Give an example of a nonlinear function.

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Front

What is the slope of a line in a linear function?

Back

The slope of a line in a linear function represents the rate of change of the function. It is calculated as the rise over run between two points on the line.

Front

What is the y-intercept in a linear function?

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