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

The domain of $$y = \text{log}_b(x)$$ is (0, ∞), meaning it only accepts positive real numbers.

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

The range of $$y = \text{log}_b(x)$$ is (-∞, ∞), meaning it can take any real number value.

How do you find the domain of the function $$f(x) = \text{ln}(x)$$ ?

The domain of $$f(x) = \text{ln}(x)$$ is x > 0, as the natural logarithm is only defined for positive values.

How do you graph a logarithmic function?

To graph a logarithmic function, identify key points, such as the x-intercept (where $$y=0$$ ) and asymptotes (vertical lines where the function approaches but never touches).

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

The vertical asymptote of $$y = \text{log}_b(x)$$ is at x = 0, where the function approaches negative infinity.

What is the transformation of the function $$y = \text{log}_b(x) + k$$ ?

The transformation $$y = \text{log}_b(x) + k$$ shifts the graph vertically by $$k$$ units.

What is the transformation of the function $$y = \text{log}_b(x - h)$$ ?

The transformation $$y = \text{log}_b(x - h)$$ shifts the graph horizontally to the right by $$h$$ units.

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

The point (1, 0) indicates that $$\text{log}_b(1) = 0$$ for any base $$b$$ , as any number raised to the power of 0 equals 1.

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

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

What is the relationship between logarithms and exponents?

Logarithms convert multiplication into addition, division into subtraction, and powers into multiplication, following the properties of logarithms.

What is the range of the function $$y = \text{log}_2(x + 1)$$ ?

The range of $$y = \text{log}_2(x + 1)$$ is (-∞, ∞), as it can take any real number value.

Log Graphs Flashcards

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1.

FLASHCARD QUESTION

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What is a logarithmic function?

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2.

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3.

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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What is the relationship between logarithmic and exponential functions?

Back

6.

FLASHCARD QUESTION

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What does the base of a logarithm indicate?

Back

7.

FLASHCARD QUESTION

Front

What is the effect of changing the base of a logarithm?

Back

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