Identifying Linear and Nonlinear Functions

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is a nonlinear function?

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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 be represented by equations that include exponents, roots, or other non-linear terms.

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

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A linear function will have a constant difference between the y-values for equal increments in the x-values. If the differences are not constant, the function is nonlinear.

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What does it mean for a relation to be 'not a function'?

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A relation is 'not a function' if there are any x-values that correspond to more than one y-value. This violates the definition of a function, which states that each input must have exactly one output.

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What is the slope of a linear function?

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The slope of a linear function is a measure of its steepness and direction. It is calculated as the change in y divided by the change in x (rise over run). A positive slope indicates an upward trend, while a negative slope indicates a downward trend.

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What is the y-intercept in a linear function?

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The y-intercept is the point where the graph of a linear function crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

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Can a quadratic function be linear?

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No, a quadratic function is not linear. It is represented by an equation of the form y = ax^2 + bx + c, which produces a parabolic graph.

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What is an example of a linear function?

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An example of a linear function is y = 2x + 3. This function has a constant slope of 2 and a y-intercept of 3.

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What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2. This function produces a parabolic graph and does not have a constant rate of change.

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How do you determine if a graph represents a linear function?

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To determine if a graph represents a linear function, check if the graph forms a straight line. If it curves or has any bends, it is nonlinear.