What does the term 'vertical stretch' mean in the context of exponential functions?

A vertical stretch occurs when the coefficient $$a$$ in the function $$f(x) = a \times b^x$$ is greater than 1, making the graph steeper.

How do you identify a horizontal shift in an exponential function?

A horizontal shift is identified by changes in the exponent, such as in $$f(x) = b^{(x - h)}$$ , which shifts the graph right by $$h$$ units.

What is the transformation of the function $$f(x) = 5^{(x)} - 3$$ ?

This transformation shifts the graph of $$f(x) = 5^x$$ down by 3 units.

What does the transformation $$f(x) = 2^{(x + 1)} + 2$$ represent?

This transformation shifts the graph left by 1 unit and up by 2 units.

What is the effect of changing the base of an exponential function, for example from $$f(x) = 2^x$$ to $$f(x) = 3^x$$ ?

Changing the base affects the growth rate; a larger base results in a steeper growth curve.

What is the transformation of the function $$f(x) = 3^{(x - 4)}$$ ?

This transformation shifts the graph right by 4 units.

How do you determine if an exponential function is increasing or decreasing?

An exponential function is increasing if the base $$b > 1$$ and decreasing if $$0

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

The y-intercept of an exponential function is the value of the function when $$x = 0$$ , which is $$f(0) = a \times b^0 = a$$ .

Exponential Functions Transformation [24-25] 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 the base of an exponential function determine?

Back

3.

FLASHCARD QUESTION

Front

Back

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

4.

FLASHCARD QUESTION

Front

Back

This transformation stretches the graph vertically by a factor of 3 and shifts it upward by 4 units.

5.

FLASHCARD QUESTION

Front

Back

The negative sign reflects the graph across the x-axis.

6.

FLASHCARD QUESTION

Front

Back

This transformation shifts the graph left by 2 units and down by 1 unit.

7.

FLASHCARD QUESTION

Front

What is the general form of an exponential function?

Back

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