How do you find the domain of the function $$f(x) = \text{log}_b(x - 1)$$ ?

To find the domain, set the argument of the logarithm greater than zero: $$x - 1 > 0$$ , which gives $$x > 1$$ .

What is the vertical asymptote of the function $$f(x) = \text{log}_b(x)$$ ?

The vertical asymptote of the function $$f(x) = \text{log}_b(x)$$ is at x = 0.

What is the transformation represented by $$f(x) = \text{log}_b(x - h)$$ ?

The transformation represents a horizontal shift of the graph to the right by h units.

How do you find the range of the function $$f(x) = -\text{ln}(x - 2) + 3$$ ?

The range is all real numbers because the logarithmic function can take any real value, and the negative sign and vertical shift do not restrict the range.

What is the domain and range of the function $$f(x) = \text{log}_b(x)$$ ?

Domain: x > 0; Range: all real numbers.

What is the general shape of the graph of a logarithmic function?

The graph of a logarithmic function increases slowly and approaches the vertical asymptote at x = 0.

What happens to the graph of a logarithmic function as x approaches infinity?

As x approaches infinity, the value of the logarithmic function also approaches infinity, but at a decreasing rate.

What is the base of a logarithm?

The base of a logarithm, denoted as b in $$\text{log}_b(x)$$ , is the number that is raised to a power to obtain x.

How do you solve the equation $$\text{log}_b(x) = k$$ ?

To solve $$\text{log}_b(x) = k$$ , rewrite it in exponential form: $$x = b^k$$ .

What is the significance of the point (1,0) on the graph of a logarithmic function?

The point (1,0) is significant because it represents the value of the logarithm when the input is equal to the base raised to the power of 0.

Graphing Logarithmic Functions Flashcard

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the Domain of a logarithmic function?

Back

2.

FLASHCARD QUESTION

Front

What is the Range of a logarithmic function?

Back

The range of a logarithmic function is all real numbers, as logarithmic functions can take any real value as output.

Tags

CCSS.HSF-IF.C.7E

3.

FLASHCARD QUESTION

Front

What is the relationship between logarithmic functions and exponential functions?

Back

Tags

CCSS.HSF.BF.B.5

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

6.

FLASHCARD QUESTION

Front

Back

A negative sign reflects the graph of the logarithmic function across the x-axis.

Tags

CCSS.HSF-IF.C.7E

7.

FLASHCARD QUESTION

Front

Back

The transformation represents a vertical shift of the graph by k units.

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