What is a concave up function?

A function is concave up if its second derivative is positive, indicating that the graph of the function opens upwards.

What is a concave down function?

A function is concave down if its second derivative is negative, indicating that the graph of the function opens downwards.

What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in $$\text{log}_b(a)$$ , $$b$$ is the base.

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

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

What is the relationship between exponential and logarithmic functions?

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

What is the significance of the point where a logarithmic function equals 1?

The point where a logarithmic function equals 1 indicates that the input value is equal to the base of the logarithm, since $$\text{log}_b(b) = 1$$ .

What is the domain of a logarithmic function?

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

What is the range of a logarithmic function?

The range of a logarithmic function $$f(x) = \text{log}_b(x)$$ is all real numbers, i.e., $$(-\text{∞}, \text{∞})$$ .

AP Precalculus Unit2B Test Prep (2.9-2.14) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

3.

FLASHCARD QUESTION

Front

What is the product property of logarithms?

Back

4.

FLASHCARD QUESTION

Front

What is the quotient property of logarithms?

Back

5.

FLASHCARD QUESTION

Front

What is the power property of logarithms?

Back

6.

FLASHCARD QUESTION

Front

What is the definition of a vertical translation of a function?

Back

A vertical translation shifts the graph of a function up or down by adding or subtracting a constant value from the function.

7.

FLASHCARD QUESTION

Front

What is the definition of a horizontal translation of a function?

Back

A horizontal translation shifts the graph of a function left or right by adding or subtracting a constant value from the input variable.

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