Piece Wise Functions Practice Test

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What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of the input variable.

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How do you calculate the average rate of change of a function on an interval [a, b]?

Back

The average rate of change is calculated using the formula: \( \frac{f(b) - f(a)}{b - a} \).

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What does g(4) represent in the context of a piecewise function?

Back

g(4) represents the value of the function at x = 4, which indicates the vertical position of the character at that horizontal position.

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What is the significance of the vertical position g(x) in a piecewise function?

Back

The vertical position g(x) represents the output value of the function, which can indicate height, distance, or other measurements depending on the context.

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Back

To graph this equation, identify the vertex, plot points, and consider the transformations such as reflection and vertical shift.

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What does the notation g(7) = 4 imply about the piecewise function?

Back

It implies that when the horizontal position x is 7, the vertical position g(x) is 4.

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Back

The absolute value creates a V-shaped graph, reflecting the values of y for negative inputs and scaling them by -2.

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What is the domain of a piecewise function?

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The domain of a piecewise function is the set of all possible input values (x) for which the function is defined.

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What is the range of a piecewise function?

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The range of a piecewise function is the set of all possible output values (g(x)) that the function can produce.

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How do you determine the intervals for a piecewise function?

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Intervals are determined by the conditions specified in the function's definition, which dictate which expression to use for given input values.