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

Multiplying an exponential function by a constant affects the vertical stretch or compression of the graph. For example, $$y = a \times b^x$$ stretches the graph vertically if $$a > 1$$ and compresses it if $$0

How do you write an exponential function from a table of values?

To write an exponential function from a table, identify the initial value (when $$x = 0$$ ) and the growth/decay factor by examining the ratio of consecutive values.

What does it mean for an exponential function to translate up or down?

Translating an exponential function up or down involves adding or subtracting a constant from the entire function. For example, $$y = b^x + k$$ translates the graph up by $$k$$ units if $$k > 0$$ .

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

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

How do you determine the direction of transformation for an exponential function?

The direction of transformation for an exponential function can be determined by the sign of the constant added or subtracted from the exponent or the function itself.

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

A negative exponent in an exponential function indicates a reciprocal relationship, leading to decay. For example, $$y = a \times b^{-x} = \frac{a}{b^x}$$ .

How can you tell if a function is exponential from a graph?

A function is exponential if its graph shows a constant percentage rate of change, characterized by a J-shaped curve that rises or falls steeply.

Writing & Transformations - Exponentials 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 it mean for a function to exhibit exponential growth?

Back

3.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit exponential decay?

Back

4.

FLASHCARD QUESTION

Front

How do you identify the base of an exponential function?

Back

5.

FLASHCARD QUESTION

Front

What is the parent function of exponential functions?

Back

6.

FLASHCARD QUESTION

Front

What transformation occurs when you add a constant to the exponent of an exponential function?

Back

7.

FLASHCARD QUESTION

Front

What transformation occurs when you subtract a constant from the exponent of an exponential function?

Back

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