5.2.1 Graphing Exponential Functions Flashcards Preview

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Flashcards in 5.2.1 Graphing Exponential Functions Deck (13):
1

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.

2

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.

3

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.

4

Given f (x) = 2^−x, evaluate f (−1)

2

5

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.

6

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.

7

Given f (x) = 3^x, evaluate f (0).

1

8

Given f (x) = 2^x, evaluate f (−1).

1/2

9

Given f (x) = e ^2x, evaluate f (3).

e^6

10

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

{y | y > 0}

11

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

N^A+B

12

Given f (x) = 3^x, evaluate f (4).

81

13

What is the domain of the function
f (x) = 2^x?

{R}

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