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

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

What does the number in front of an exponential function represent?

The number in front of an exponential function, such as in $$y = a \times b^x$$ , represents the initial value or vertical stretch factor.

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 value of $$\text{log}_3(9)$$ ?

$$\text{log}_3(9) = 2$$ because $$3^2 = 9$$ .

What is the domain of the inverse function of $$f(x) = \text{log}_3(x)$$ ?

The domain of the inverse function of $$f(x) = \text{log}_3(x)$$ is $$(-\text{∞}, \text{∞})$$ .

How do you graph an exponential function?

To graph an exponential function, identify the y-intercept (when $$x=0$$ ), determine the growth or decay based on the base, and plot additional points.

What is the solution to the equation $$\text{log}_3(x + 2) = 2$$ ?

The solution is $$x = 7$$ , since $$3^2 = x + 2$$ leads to $$x = 9 - 2 = 7$$ .

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

Changing the base of a logarithm affects the steepness of the graph but not the overall shape. For example, $$\text{log}_2(x)$$ grows faster than $$\text{log}_3(x)$$ .

What is a decreasing exponential function?

A decreasing exponential function is of the form $$f(x) = a \times b^x$$ where $$0

Review - Unit 4 Exponential and Logarithmic Functions

Flashcard

•

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?

Back

FLASHCARD QUESTION

Front

What is the general form of a logarithmic function?

Back

Tags

CCSS.HSF-IF.C.7E

FLASHCARD QUESTION

Front

What is the inverse of an exponential function?

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

What does the base of an exponential function determine?

Back

Tags

CCSS.HSF-IF.C.8B

FLASHCARD QUESTION

Front

What is the domain of a logarithmic function?

Back

FLASHCARD QUESTION

Front

What is the range of an exponential function?

Back

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.B.5

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