Linear vs Non-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.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be a curve or any other shape that is not linear.

Front

How can you identify a linear equation from its graph?

Back

A linear equation can be identified by its graph being a straight line, with a constant slope throughout.

Front

What is the general form of a linear equation in two variables?

Back

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

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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).

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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 the function when x = 0.

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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.

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What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include quadratic functions (e.g., f(x) = x^2), exponential functions (e.g., f(x) = 2^x), and trigonometric functions (e.g., f(x) = sin(x)).

Front

How can you determine if a table of values represents a linear function?

Back

A table of values represents a linear function if the differences between consecutive y-values are constant for equal intervals of x.

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What is the significance of the degree of a polynomial in determining linearity?

Back

The degree of a polynomial indicates its highest exponent. A polynomial of degree 1 is linear, while a polynomial of degree greater than 1 is nonlinear.