Functions Unit Review

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What is the Domain of a linear function?

Back

The domain of a linear function is the set of all possible input values (x-values) for which the function is defined. For example, for the function defined as -6 ≤ x ≤ 6, the domain includes all real numbers between -6 and 6.

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How do you calculate the average rate of change of a function?

Back

The average rate of change of a function f from x = a to x = b is calculated using the formula: (f(b) - f(a)) / (b - a). This represents the change in the function's value divided by the change in the input.

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value). In other words, for every x in the domain, there is one and only one corresponding y.

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What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each element of the domain is paired with an element of the range. It helps to determine if a relation is a function.

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What is the Range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, if a function can output any real number, its range is all real numbers.

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

Back

A relation is 'not a function' if at least one input (x-value) is associated with more than one output (y-value). This violates the definition of a function.

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What is the significance of the average rate of change being negative?

Back

A negative average rate of change indicates that the function is decreasing over the interval considered. This means that as the input increases, the output decreases.

Front

What is the difference between discrete and continuous functions?

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Discrete functions have distinct, separate values (often represented as points), while continuous functions have an unbroken range of values (represented as a line or curve).

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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 the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x). It indicates how much y changes for a unit change in x.