What is the inverse function of $$g(x) = 5^{(x-3)} - 2$$ ?

$$g^{-1}(x) = \text{log}_5(x + 2) + 3$$

What is the inverse function of $$2\text{log}_5(x - 3)$$ ?

$$f^{-1}(x) = 5^{\frac{x}{2}} + 3$$

What is the relationship between exponential and logarithmic functions?

Exponential functions are the inverse of logarithmic functions.

What is the parent function of logarithmic functions?

The parent function is $$f(x) = \text{log}_b(x)$$ where b > 0 and b ≠ 1.

What does the transformation 'Translate up 2' mean for the function $$f(x) = \text{log}_2(x)$$ ?

It means the graph of the function is shifted 2 units upwards.

What does the transformation 'Translate down 3' mean for the function $$f(x) = \text{log}_2(x)$$ ?

It means the graph of the function is shifted 3 units downwards.

How do you find the inverse of a function algebraically?

To find the inverse, swap the x and y variables and solve for y.

What is the effect of adding a constant to the argument of a logarithmic function?

Adding a constant translates the graph horizontally.

What is the effect of multiplying a logarithmic function by a constant?

Multiplying by a constant vertically stretches or compresses the graph.

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

The domain is all positive real numbers, $$x > 0$$ .

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

The range is all real numbers, $$(-\text{∞}, \text{∞})$$ .

Transformations and Inverse of Log and Exp Functions Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

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2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

Translate right 2

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

Translate left 3

6.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

7.

FLASHCARD QUESTION

Front

Back

The base is 5.

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