What is the initial value of the function $$f(x) = 6(0.5)^x$$ ?

The initial value (y-intercept) is 6, which is the value of $$f(0)$$ .

What is the equation of the asymptote for the function $$f(x) = 13(0.27)^x$$ ?

The equation of the asymptote is $$y = 0$$ .

What does it mean for an exponential function to have a y-intercept at a certain point?

Having a y-intercept at a certain point means that the graph of the function crosses the y-axis at that value when $$x = 0$$ .

What is the general form of an exponential decay function?

The general form of an exponential decay function is $$f(x) = a \times b^x$$ , where $$0

How can you identify the y-intercept from the equation of an exponential function?

You can identify the y-intercept by evaluating the function at $$x = 0$$ , which gives you $$f(0) = a$$ .

What is the significance of the base in the function $$f(x) = 125(5)^x$$ ?

The base 5 indicates that the function grows rapidly as $$x$$ increases, representing exponential growth.

What does the term 'exponential growth' refer to?

Exponential growth refers to an increase in a quantity where the rate of growth is proportional to the current amount, typically modeled by a function with a base greater than 1.

What does the term 'exponential decay' refer to?

Exponential decay refers to a decrease in a quantity where the rate of decay is proportional to the current amount, typically modeled by a function with a base between 0 and 1.

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

To write the equation, identify the y-intercept (initial value) and the base by observing the growth or decay rate of the graph.

What is the relationship between the y-intercept and the initial value in an exponential function?

The y-intercept is the initial value of the function when $$x = 0$$ , representing the starting point of the exponential growth or decay.

Key Features of Exponential functions Flashcards

Student preview

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 determine?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What is the y-intercept of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

4.

FLASHCARD QUESTION

Front

What is the horizontal asymptote of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

How do you determine if an exponential function is increasing or decreasing?

Back

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.LE.B.5

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

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