Identify and Compare Functions

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.

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. Its general form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear 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 determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, then it is not a function.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

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What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

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What is a table of values in relation to functions?

Back

A table of values lists pairs of input (x) and output (y) values, showing how the function behaves for different inputs.

Front

What is the significance of the equation y = 1/3 x - 4?

Back

This equation represents a linear function with a slope of 1/3 and a y-intercept of -4.

Front

What does it mean if a table does not represent a function?

Back

If a table does not represent a function, it means that at least one input value corresponds to multiple output values.