What is the significance of the constant 'a' in an exponential function?

The constant 'a' in an exponential function represents the initial value or the y-intercept of the function.

How do you write an exponential function given a point and the base?

If you have a point (x, y) and the base $$b$$ , you can write the function as $$f(x) = y / b^x$$ .

What is the relationship between exponential functions and their inverses?

The inverse of an exponential function is a logarithmic function. For example, if $$f(x) = b^x$$ , then its inverse is $$f^{-1}(x) = \text{log}_b(x)$$ .

How do you find the value of an exponential function at a specific point?

To find the value of an exponential function at a specific point, substitute the x-value into the function and calculate the result.

What is the effect of changing the base of an exponential function?

Changing the base of an exponential function affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 0) results in slower growth.

How can you tell if a function is exponential by looking at its graph?

A function is exponential if its graph shows a constant percentage increase or decrease, resulting in a J-shaped curve for growth or a decreasing curve for decay.

What is the formula for converting an exponential function to logarithmic form?

The formula for converting an exponential function $$b^y = x$$ to logarithmic form is $$y = \text{log}_b(x)$$ .

How do you determine the growth factor from an exponential function?

The growth factor of an exponential function $$f(x) = a \times b^x$$ is the base $$b$$ , which indicates how much the function multiplies by for each unit increase in $$x$$ .

Writing Exponential Functions from Tables & Graphs Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the base of an exponential function represent?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

How do you identify an exponential function from a table of values?

Back

To identify an exponential function from a table, check if the ratio of consecutive outputs is constant when the inputs are increased by the same amount.

Tags

CCSS.HSF-LE.A.1A

4.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

Tags

CCSS.HSF-LE.A.1A

5.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

Tags

CCSS.HSF-LE.A.1A

6.

FLASHCARD QUESTION

Front

How can you determine the equation of an exponential function from a graph?

Back

Tags

CCSS.HSF.LE.A.2

7.

FLASHCARD QUESTION

Front

What does the y-intercept of an exponential function represent?

Back

Tags

CCSS.HSF-IF.C.7E

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