What is a horizontal shift in the context of function transformations?

A horizontal shift occurs when the graph of a function is moved left or right. For example, $$f(x) = b^{x + c}$$ shifts the graph left by 'c' units.

What is a vertical shift in the context of function transformations?

A vertical shift occurs when the graph of a function is moved up or down. For example, $$f(x) = b^x + k$$ shifts the graph up by 'k' units.

What is the domain of an exponential function?

The domain of an exponential function is all real numbers, expressed as $$(-\text{∞}, \text{∞})$$ .

What is the range of an exponential function?

The range of an exponential function is all positive real numbers, expressed as $$(0, \text{∞})$$ .

How do you solve the equation $$\text{log}_6(3x - 2) = \text{log}_6(5x - 8)$$ ?

Set the arguments equal: $$3x - 2 = 5x - 8$$ . Solve for 'x' to find $$x = 3$$ .

What is the value of $$\text{log}_3(81)$$ ?

$$\text{log}_3(81) = 4$$ because $$3^4 = 81$$ .

What is the effect of a negative exponent in exponential functions?

A negative exponent indicates a reciprocal. For example, $$b^{-n} = \frac{1}{b^n}$$ .

What is the significance of the y-intercept in an exponential function?

The y-intercept of an exponential function is the value of the function when $$x = 0$$ , which is $$y = a$$ .

Algebra II - Exponential and Logarithmic Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the base of a logarithm?

Back

3.

FLASHCARD QUESTION

Front

What is the relationship between exponential and logarithmic functions?

Back

4.

FLASHCARD QUESTION

Front

Back

In the formula, 'r' represents the rate of growth.

5.

FLASHCARD QUESTION

Front

Back

In the formula, 'r' represents the rate of decay.

6.

FLASHCARD QUESTION

Front

How do you convert an exponential equation to logarithmic form?

Back

7.

FLASHCARD QUESTION

Front

What is the parent function of exponential functions?

Back

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