What is the equation of the horizontal asymptote for the function $$f(x) = a \times b^x + c$$ ?

The horizontal asymptote is $$y = c$$ .

How do you find the y-intercept of the function $$f(x) = 3 \times 2^x$$ ?

The y-intercept is found by evaluating $$f(0) = 3 \times 2^0 = 3$$ .

What is the relationship between the bases in the equation $$9^{8-x} = 27^{x-3}$$ ?

Both sides can be expressed with base 3: $$9 = 3^2$$ and $$27 = 3^3$$ .

How do you determine the horizontal asymptote of the function $$f(x) = 2^x - 1$$ ?

The horizontal asymptote is $$y = -1$$ .

What is the solution to the equation $$8 = 2^{5x+7}$$ ?

The solution is $$x = -\frac{4}{5}$$ .

What does it mean for a function to be increasing or decreasing?

A function is increasing if its output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

What is the base of an exponential function?

The base of an exponential function is the constant $$b$$ in the function $$f(x) = a \times b^x$$ , which determines the rate of growth or decay.

How can you express the equation $$2^x = 8$$ in logarithmic form?

In logarithmic form, it is expressed as $$x = \text{log}_2(8)$$ .

Exponential Functions Flashcard

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the y-intercept of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

3.

FLASHCARD QUESTION

Front

What is the general shape of the graph of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

4.

FLASHCARD QUESTION

Front

What is a horizontal asymptote in the context of exponential functions?

Back

Tags

CCSS.HSF-IF.C.7D

5.

FLASHCARD QUESTION

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation to have the same base.

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

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