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

The domain of the function $$y = \text{log}_b(x)$$ is $$x > 0$$ .

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

The range of the function $$y = \text{log}_b(x)$$ is all real numbers, or $$(-\text{∞}, \text{∞})$$ .

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

The x-intercept occurs when $$y = 0$$ , which means $$x = b$$ .

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

The y-intercept does not exist because the logarithmic function is undefined for $$x

What is an asymptote in the context of logarithmic functions?

An asymptote is a line that the graph approaches but never touches. For logarithmic functions, the vertical asymptote is at $$x = 0$$ .

How do you graph the function $$y = \text{log}_b(x)$$ ?

To graph $$y = \text{log}_b(x)$$ , plot points for various values of $$x$$ , noting that the graph passes through the point (b, 1) and approaches the vertical asymptote at $$x = 0$$ .

What is the relationship between exponential and logarithmic functions?

Exponential and logarithmic functions are inverses of each other. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

What is the change of base formula for logarithms?

The change of base formula states that $$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any positive base $$k$$ .

What is the product rule for logarithms?

The product rule states that $$\text{log}_b(xy) = \text{log}_b(x) + \text{log}_b(y)$$ .

What is the quotient rule for logarithms?

The quotient rule states that $$\text{log}_bigg(\frac{x}{y}igg) = \text{log}_b(x) - \text{log}_b(y)$$ .

What is the power rule for logarithms?

The power rule states that $$\text{log}_b(x^k) = k \times \text{log}_b(x)$$ .

How do you find the inverse of a logarithmic function?

To find the inverse of a logarithmic function, switch the roles of $$x$$ and $$y$$ and solve for $$y$$ . For example, the inverse of $$y = \text{log}_b(x)$$ is $$x = b^y$$ .

Graphing Exponential and Logarithmic Functions

Flashcard

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Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-IF.C.7E, HSF.BF.B.5, HSF-BF.B.4A

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FLASHCARD QUESTION

Front

What is an exponential function?

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FLASHCARD QUESTION

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What is a logarithmic function?

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CCSS.HSF-IF.C.7E

FLASHCARD QUESTION

Front

What is the base of a logarithm?

Back

Tags

CCSS.HSF.BF.B.5

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

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