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

To determine the equation from a graph, identify the y-intercept (initial value) and the rate of change (slope) to find the base $$b$$ .

What is the y-intercept of an exponential function?

The y-intercept of an exponential function is the point where the graph crosses the y-axis, which occurs at $$f(0) = a$$ .

What does it mean if an exponential function has a negative base?

An exponential function cannot have a negative base in real numbers, as it would not produce a valid output for all real values of $$x$$ .

How do you write an exponential function given a specific point?

To write an exponential function given a specific point, use the point to solve for $$a$$ or $$b$$ in the equation $$f(x) = a \times b^x$$ .

What is the relationship between exponential functions and their graphs?

Exponential functions have graphs that are continuous and either increase or decrease rapidly, depending on whether they represent growth or decay.

What is the formula for finding the growth factor in an exponential function?

The growth factor can be found using the formula $$b = \frac{f(x_1)}{f(x_0)}$$ , where $$x_1$$ and $$x_0$$ are two consecutive x-values.

How can you verify if a function is exponential using a graph?

You can verify if a function is exponential by checking if the graph shows a consistent curvature, indicating a constant multiplicative rate of change.

What is the importance of exponential functions in real-world applications?

Exponential functions are important in modeling real-world phenomena such as population growth, radioactive decay, and interest calculations.

Warm-up versioWriting Exponential Functions from Tables & Graphs Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the base of an exponential function represent?

Back

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 remains constant when the inputs are increased by the same amount.

4.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

5.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

6.

FLASHCARD QUESTION

Front

How can you convert a table of values into an exponential function?

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the initial value in an exponential function?

Back

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