How do you determine the transformation from $$f(x) = 3^x$$ to $$g(x) = 3^x - 4$$ ?

The transformation is a vertical shift down by 4 units.

What is the general form of an exponential decay function?

An exponential decay function can be expressed as $$f(x) = a \times b^{-x}$$ , where $$0

What does the term 'parent function' refer to in exponential functions?

The parent function of exponential functions is $$f(x) = b^x$$ , which serves as the basic form for transformations.

How does changing the base of an exponential function affect its graph?

Changing the base affects the rate of growth or decay; larger bases grow faster, while bases between 0 and 1 decay faster.

What is the significance of the y-intercept in exponential functions?

The y-intercept indicates the initial value of the function when $$x = 0$$ , which is crucial for understanding growth or decay.

What transformation occurs when you multiply an exponential function by a negative number?

Multiplying by a negative number reflects the graph across the x-axis.

How do you find the equation of an exponential function given a transformation?

Identify the transformations (shifts, stretches) and apply them to the parent function to derive the new equation.

What is the effect of a negative exponent in an exponential function?

A negative exponent indicates a reciprocal, transforming $$b^{-x}$$ into $$\frac{1}{b^x}$$ , which represents exponential decay.

6.6 Transformations of Exponential Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the base of an exponential function?

Back

3.

FLASHCARD QUESTION

Front

What is the y-intercept of an exponential function?

Back

4.

FLASHCARD QUESTION

Front

How does a vertical stretch affect an exponential function?

Back

5.

FLASHCARD QUESTION

Front

What does a horizontal shift of an exponential function entail?

Back

6.

FLASHCARD QUESTION

Front

What is the effect of a vertical shift on an exponential function?

Back

7.

FLASHCARD QUESTION

Front

Back

The transformation is a horizontal shift to the right by 3 units.

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