What does the base $$b$$ represent in an exponential function?

The base $$b$$ determines the rate of growth or decay of the function. If $$b > 1$$ , the function represents exponential growth; if $$0

What is the effect of changing the value of $$a$$ in an exponential function?

Changing the value of $$a$$ affects the vertical stretch or compression of the graph. A larger $$a$$ value stretches the graph, while a smaller $$a$$ value compresses it.

What does the graph of an exponential function look like?

The graph of an exponential function is a smooth curve that either rises steeply (growth) or falls steeply (decay) as $$x$$ increases.

What is the horizontal asymptote of an exponential function?

The horizontal asymptote of an exponential function is the line $$y = 0$$ , which the graph approaches but never touches.

How do you find the y-intercept of the function $$y = \frac{1}{2} \times 4^x$$ ?

To find the y-intercept, evaluate $$y$$ at $$x = 0$$ : $$y = \frac{1}{2} \times 4^0 = \frac{1}{2} \times 1 = \frac{1}{2}$$ .

What is the y-intercept of the function $$f(x) = 2(3^x)$$ ?

The y-intercept is found by evaluating $$f(0) = 2(3^0) = 2(1) = 2$$ .

What does it mean if a function has a base of $$b = 5$$ ?

If a function has a base of $$b = 5$$ , it indicates exponential growth, as $$b > 1$$ .

What is the difference between exponential growth and decay?

Exponential growth occurs when the base $$b > 1$$ , leading to increasing values as $$x$$ increases. Exponential decay occurs when $$0

How can you identify exponential functions from a set of graphs?

Exponential functions will show a rapid increase or decrease and will have a characteristic curve, unlike linear or quadratic functions.

What is the significance of the point (0, a) in the graph of an exponential function?

The point (0, a) represents the y-intercept of the function, indicating the initial value of the function when $$x = 0$$ .

Graphing Exponential Functions Flashcards

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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What is the y-intercept of an exponential function?

Back

4.

FLASHCARD QUESTION

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

Back

5.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

6.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

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7.

FLASHCARD QUESTION

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