What is the transformation of the function $$y = 2^{(x-2)}$$ ?

The function $$y = 2^{(x-2)}$$ represents a horizontal translation to the right by 2 units of the base function $$y = 2^x$$ .

What is the transformation of the function $$y = 4^x - 2$$ ?

The function $$y = 4^x - 2$$ represents a vertical translation down by 2 units of the base function $$y = 4^x$$ .

How do you represent a 35% increase in an exponential growth model?

To represent a 35% increase, use the model $$y = a(1 + r)^x$$ , where $$r = 0.35$$ . For an initial amount of 15, the function is $$y = 15(1.35)^x$$ .

What is the general form of an exponential decay function?

The general form of an exponential decay function is $$y = a \times b^{-x}$$ , where $$0

What does the term 'initial amount' refer to in exponential functions?

The initial amount is the value of the function when $$x = 0$$ . It represents the starting point of the growth or decay process.

What is the transformation of the function $$y = 2^{(x+3)}$$ ?

The function $$y = 2^{(x+3)}$$ represents a horizontal translation to the left by 3 units of the base function $$y = 2^x$$ .

What is the effect of multiplying an exponential function by a constant?

Multiplying an exponential function by a constant results in a vertical stretch or compression. For example, $$y = 3 \times 2^x$$ stretches the graph vertically by a factor of 3.

What is the significance of the exponent in an exponential function?

The exponent in an exponential function determines the rate of growth or decay. A larger exponent results in a steeper curve, indicating faster growth or decay.

How do you identify the transformations of a given exponential function?

To identify transformations, compare the given function to the base function $$y = a \times b^x$$ and note changes in the exponent and constant terms.

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 does a vertical translation of a function mean?

Back

3.

FLASHCARD QUESTION

Front

What does a horizontal translation of a function mean?

Back

4.

FLASHCARD QUESTION

Front

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

Back

The base determines the rate of growth or decay. A base greater than 1 (e.g., 2) indicates exponential growth, while a base between 0 and 1 (e.g., 0.5) indicates exponential decay.

5.

FLASHCARD QUESTION

Front

What is the effect of adding a constant to an exponential function?

Back

6.

FLASHCARD QUESTION

Front

What is the effect of subtracting a constant from an exponential function?

Back

7.

FLASHCARD QUESTION

Front

Back

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