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AP Calculus AB: 5.2.1 Graphing Exponential Functions

Mathematics13 CardsCreated 12 months ago

This flashcard set explains the key properties of exponential functions, focusing on how the base affects the graph's shape. It includes notes on transformations like reflection across the y-axis and evaluates specific exponential expressions. Graph identification and function evaluation are used to reinforce understanding.

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Graphing Exponential Functions

  • An exponential function has the variable in the exponent, not in the base.

  • An exponential function cannot have a negative base. Exponential functions with positive bases less than 1 have graphs that are decreasing.

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Key Terms

Term
Definition

Graphing Exponential Functions

  • An exponential function has the variable in the exponent, not in the base.

  • An exponential function cannot have a negative ba...

note

  • An exponential function is a function whose variable is in the exponent.

  • To graph an exponential function, try plotting some...

Which of the following is the graph of the function f(x)=3^−x?

Notice that any x-term you plug in will be multiplied by negative one. The result of this operation is that the entire exponential graph is going t...

Given f (x) = 2^−x, evaluate f (−1)

2

Which of the following is the graph of y = 3^x?

The function is an exponential function with base 3. When x = 0, the function value is 1. When x = 1, the function value is 3. When x = 2, the func...

Which of the following is the graph of  f (x) = 2^x?

The function is an exponential function with base 2. When x = 0 the function equals 1. When x = 1 the function equals 2. When x = 2 the function eq...

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AP Calculus AB: 5.2.1 Graphing Exponential Functions
TermDefinition

Graphing Exponential Functions

  • An exponential function has the variable in the exponent, not in the base.

  • An exponential function cannot have a negative base. Exponential functions with positive bases less than 1 have graphs that are decreasing.

note

  • An exponential function is a function whose variable is in the exponent.

  • To graph an exponential function, try plotting some points.

  • Remember, a number raised to a negative power moves into the denominator.

  • All exponential functions have the same basic shape, but the value of the base does affect the appearance of the curve.

  • For larger bases, the graph becomes very steep in the first quadrant. However, in the second quadrant the graph is very flat. Notice that the graph is always increasing.

  • As the base becomes smaller, the curve becomes less steep in the first quadrant.

  • For bases less than one but greater than zero, the graph reflects across the y-axis.

  • The exponential function is not defined for negative bases.

Which of the following is the graph of the function f(x)=3^−x?

Notice that any x-term you plug in will be multiplied by negative one. The result of this operation is that the entire exponential graph is going to ‘flip’ across the y‑axis. So answer B best reflects the given curve.

Given f (x) = 2^−x, evaluate f (−1)

2

Which of the following is the graph of y = 3^x?

The function is an exponential function with base 3. When x = 0, the function value is 1. When x = 1, the function value is 3. When x = 2, the function value is 9.

Which of the following is the graph of  f (x) = 2^x?

The function is an exponential function with base 2. When x = 0 the function equals 1. When x = 1 the function equals 2. When x = 2 the function equals 4. Plot a few more points and you will see that only answer B matches all the points you plot.

Given f (x) = 3^x, evaluate f (0).

1

Given f (x) = 2^x, evaluate f (−1).

1/2

Given f (x) = e ^2x, evaluate f (3).

e^6

What is the range of the function f(x)=4^−x?

{y | y > 0}

Which of the following statements is equal to N^A⋅N^B?

N^A+B

Given f (x) = 3^x, evaluate f (4).

81

What is the domain of the function

f (x) = 2^x?

{R}