What is the horizontal asymptote of the function $$f(x) = 3igg(\frac{11}{7}igg)^x - 12$$ ?

The horizontal asymptote is $$y = -12$$ , as the function approaches this value as $$x$$ approaches negative infinity.

What does the transformation $$f(x) = a \times b^x + c$$ do to the graph?

The transformation shifts the graph vertically by $$c$$ units. If $$c > 0$$ , the graph shifts up; if $$c

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

An exponential function is increasing if the base $$b > 1$$ and decreasing if $$0

What is the significance of the constant $$a$$ in the function $$f(x) = a \times b^x$$ ?

The constant $$a$$ represents the initial value or the y-intercept of the function when $$x = 0$$ .

How do you graph an exponential function?

To graph an exponential function, plot the y-intercept, calculate additional points by choosing values for $$x$$ , and draw a smooth curve through the points.

What is the domain and range of an exponential function?

The domain of an exponential function is all real numbers ( $$(-\text{∞}, \text{∞})$$ ), and the range is all real numbers greater than the horizontal asymptote.

What is the relationship between exponential functions and their inverses?

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

How do you solve exponential equations?

To solve exponential equations, you can take the logarithm of both sides or rewrite the equation in a form that allows you to isolate the variable.

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

Exponential functions model many real-world phenomena, such as population growth, radioactive decay, and interest calculations in finance.

Graphing Exponential Functions 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 determine?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

How do you identify the y-intercept of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

4.

FLASHCARD QUESTION

Front

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

Back

The graph of an exponential function is a smooth curve that either increases or decreases rapidly, approaching the x-axis but never touching it (asymptote).

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

6.

FLASHCARD QUESTION

Front

How do you find the table of values for an exponential function?

Back

Tags

CCSS.HSF-LE.A.1A

7.

FLASHCARD QUESTION

Front

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

Back

Changing the base affects the steepness of the graph. A larger base results in a steeper curve, while a smaller base (greater than 0 but less than 1) results in a flatter curve.

Tags

CCSS.HSF-IF.C.7E

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