Identify Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is a non-linear function?

Back

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

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation f(x) = mx + b. It indicates how much y changes for a unit change in x.

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by 'b' in the equation f(x) = mx + b.

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How can you determine if a function is linear from its graph?

Back

A function is linear if its graph is a straight line. If the graph curves or has any bends, the function is non-linear.

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What is the general form of a linear equation?

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The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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What is the difference between a linear function and a linear equation?

Back

A linear function describes a relationship between variables that can be graphed as a line, while a linear equation is a mathematical statement that two expressions are equal.

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Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line and the output value (y) remains constant regardless of the input value (x).

Front

What is an example of a non-linear function?

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An example of a non-linear function is f(x) = x^2, which represents a parabola when graphed.

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How do you identify a linear function from a table of values?

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A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, the function is linear.