Identify Function Characteristics

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What is a constant function?

Back

A constant function is a function that does not change its value regardless of the input. It is represented as f(x) = c, where c is a constant.

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What does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line. This means that the change in y is proportional to the change in x, resulting in a constant rate of change.

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What is the definition of a discrete function?

Back

A discrete function is a function that has distinct, separate values. It is not continuous and is often represented by a set of individual points.

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What is the definition of a continuous function?

Back

A continuous function is a function that does not have any breaks, jumps, or holes in its graph. It can be drawn without lifting the pencil from the paper.

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How do you determine the interval where a function is increasing?

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A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

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What is the significance of the interval notation 3 < x < 5?

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The interval notation 3 < x < 5 indicates that x can take any value between 3 and 5, but not including 3 and 5 themselves.

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What does it mean for a function to be nonlinear?

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A nonlinear function is one that does not form a straight line when graphed. This means the rate of change is not constant.

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What is the role of the x and y coordinates in determining linearity?

Back

In a linear function, the x and y coordinates change at a constant rate, meaning the ratio of the change in y to the change in x remains the same.

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What is an example of a function that is not a function?

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An example of a relation that is not a function is the set of points {(1,2), (1,3)}, where the input 1 corresponds to two different outputs.