Identifying Linear Functions

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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. 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 nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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

Back

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 the same, the function is linear.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

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What is the y-intercept 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 the value of b in the equation f(x) = mx + b.

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Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the x-value increases, the y-value decreases.

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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 = 0, where A, B, and C are constants.

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

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

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A function is linear if its graph is a straight line. If the graph curves or bends, the function is nonlinear.

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What is an example of a linear function?

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An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.