What is the graph of $$f(x) = 3^x$$ ?

The graph of $$f(x) = 3^x$$ represents exponential growth, starting from the point (0,1) and rising steeply as x increases.

What is the graph of $$f(x) = (\frac{1}{3})^x$$ ?

The graph of $$f(x) = (\frac{1}{3})^x$$ represents exponential decay, starting from the point (0,1) and falling steeply as x increases.

What is the logarithmic function?

A logarithmic function is of the form $$f(x) = \log_a(x)$$ , which answers the question: to what power must the base $$a$$ be raised to produce $$x$$ .

What is the domain of a logarithmic function?

The domain of a logarithmic function $$f(x) = \log_a(x)$$ is all positive real numbers, i.e., $$x > 0$$ .

What is the range of an exponential function?

The range of an exponential function $$f(x) = a^x$$ is all positive real numbers, i.e., $$f(x) > 0$$ .

What is the value of $$\log_3(9)$$ ?

The value of $$\log_3(9)$$ is 2, because $$3^2 = 9$$ .

What is the value of $$\log_5(25)$$ ?

The value of $$\log_5(25)$$ is 2, because $$5^2 = 25$$ .

How do you find the inverse of $$f(x) = 5^x$$ ?

To find the inverse, set $$y = 5^x$$ , then solve for $$x$$ : $$x = \log_5(y)$$ , so the inverse is $$f^{-1}(x) = \log_5(x)$$ .

What is the graph of a logarithmic function?

The graph of a logarithmic function increases slowly and approaches the y-axis but never touches it, starting from the point (1,0).

Practice: Exponential and Logarithmic Graphs 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 is the base of a logarithm?

Back

Tags

CCSS.HSF.BF.B.5

3.

FLASHCARD QUESTION

Front

What is the inverse of an exponential function?

Back

Tags

CCSS.HSF-BF.B.4A

4.

FLASHCARD QUESTION

Front

How do you classify exponential growth?

Back

Exponential growth occurs when the value of a function increases rapidly as the input increases, typically represented by a graph that rises steeply.

Tags

CCSS.HSF-IF.C.8B

5.

FLASHCARD QUESTION

Front

How do you classify exponential decay?

Back

Exponential decay occurs when the value of a function decreases rapidly as the input increases, typically represented by a graph that falls steeply.

Tags

CCSS.HSF-IF.C.8B

6.

FLASHCARD QUESTION

Front

What is the relationship between exponential and logarithmic functions?

Back

Tags

CCSS.HSF.BF.B.5

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

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