How do you represent a horizontal translation right by 3 units for the function $$y = 2^x$$ ?

To represent a horizontal translation right by 3 units, the function becomes $$y = 2^{(x - 3)}$$ .

What is the transformation from $$y = 2^x$$ to $$y = 2^{-x}$$ ?

This represents a reflection over the y-axis.

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 is the transformation from $$y = 2^x$$ to $$y = 2^x - 4$$ ?

This represents a vertical translation down by 4 units.

What is the effect of changing the base of an exponential function?

Changing the base affects the rate of growth or decay. A larger base results in faster growth, while a base between 0 and 1 results in decay.

What is the transformation from $$y = 2^x$$ to $$y = -2^x + 1$$ ?

This represents a reflection over the x-axis and a vertical translation up by 1 unit.

What does it mean for an exponential function to have a horizontal asymptote?

A horizontal asymptote is a horizontal line that the graph of the function approaches but never touches, typically at $$y = 0$$ for exponential decay functions.

What is the transformation from $$y = 2^x$$ to $$y = 2^{(x - 1)} + 3$$ ?

This represents a horizontal translation right by 1 unit and a vertical translation up by 3 units.

What is the significance of the constant $$a$$ in the exponential function $$f(x) = a \times b^x$$ ?

The constant $$a$$ represents the initial value or the y-intercept of the function when $$x = 0$$ .

Investigating 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 horizontal translation of a function mean?

Back

3.

FLASHCARD QUESTION

Front

What is a vertical translation of a function?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

This represents a horizontal translation left by 2 units.

7.

FLASHCARD QUESTION

Front

What does it mean to reflect a function over the y-axis?

Back

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