Exponential Functions Transformations

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What is an exponential function?

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What is the general form of an exponential function?

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Front

What does the base 'b' in an exponential function represent?

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The base 'b' in an exponential function determines the rate of growth or decay. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

How does a vertical shift affect the graph of an exponential function?

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Back

The range of the function is (5, ∞). The minimum value is 5, which occurs as x approaches negative infinity.

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The transformation includes a left shift of 3 units and a downward shift of 6 units.

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The y-intercept occurs when x = 0, giving the point (0, 4).

Front

What does adding a constant 'k' to an exponential function do?

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Adding a constant 'k' to an exponential function results in a vertical shift of the graph. If k > 0, the graph shifts up; if k < 0, it shifts down.

Front

What is the effect of a horizontal shift in an exponential function?

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The transformation is a right shift of 2 units.