Linear or Nonlinear Function Extra Credit

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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.

Front

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.

Front

How can you identify a linear function from its graph?

Back

A linear function will have a constant slope and will graph as a straight line. If the graph curves or changes direction, it is nonlinear.

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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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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. This indicates that the output value (y) does not change regardless of the input value (x).

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which represents a parabola. The graph of this function curves and does not form a straight line.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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

Back

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear. If the differences change, the function is nonlinear.

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

Back

A linear equation is an equation that represents a linear relationship, while a linear function is a specific type of linear equation that defines a relationship between input and output values.