What is the horizontal asymptote of the function $$f(x) = a \times b^{(x-h)} + k$$ ?

The horizontal asymptote is the line $$y = k$$ , which the graph approaches as x approaches infinity or negative infinity.

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

The base 'b' determines the rate of growth or decay. A larger base results in faster growth, while a base less than 1 results in decay.

What is the significance of the y-intercept in an exponential function?

The y-intercept is the point where the graph crosses the y-axis, indicating the initial value of the function when x = 0.

How do you find the vertical translation of an exponential function?

The vertical translation can be found by identifying the constant added or subtracted from the function. For example, in $$y = 2^x - 4$$ , the graph is translated down 4 units.

What is the relationship between exponential functions and their asymptotes?

Exponential functions approach their horizontal asymptote but never actually reach it, indicating the behavior of the function as x approaches infinity or negative infinity.

What is the difference between exponential growth and linear growth?

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount. Exponential growth is much faster over time.

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

A horizontal asymptote indicates the value that the function approaches as x approaches infinity or negative infinity, representing the limiting behavior of the function.

How can you identify the transformations of an exponential function from its equation?

By comparing the function to the general form $$y = a \times b^{(x-h)} + k$$ , you can identify vertical shifts (k), horizontal shifts (h), and reflections (if 'a' is negative).

What is the impact of changing the value of 'k' in an exponential function?

Changing the value of 'k' results in a vertical shift of the graph. If 'k' is positive, the graph shifts up; if negative, it shifts down.

Transformations of Exponential Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a vertical translation in exponential functions?

Back

Tags

CCSS.HSF.BF.B.3

2.

FLASHCARD QUESTION

Front

What is a horizontal translation in exponential functions?

Back

Tags

CCSS.HSF-IF.C.7E

3.

FLASHCARD QUESTION

Front

Back

The 'a' represents the y-intercept of the function, which is the value of y when x = 0.

Tags

CCSS.HSF.LE.B.5

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

How do you determine if a function represents exponential growth or decay?

Back

Tags

CCSS.HSF-IF.C.8B

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.8B

7.

FLASHCARD QUESTION

Front

What is the general form of an exponential function?

Back

Tags

CCSS.HSF.LE.A.2

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