5.2.1 Graphing Exponential Functions

Question 1

Graphing Exponential Functions

Answer 1

• 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.

Question 2

note

Answer 2

• 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.

Question 3

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

Answer 3

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.

Question 4

Given f (x) = 2^−x, evaluate f (−1)

Answer 4

2

Question 5

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

Answer 5

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.

Question 6

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

Answer 6

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.

Question 7

Given f (x) = 3^x, evaluate f (0).

Answer 7

1

Question 8

Given f (x) = 2^x, evaluate f (−1).

Answer 8

1/2

Question 9

Given f (x) = e ^2x, evaluate f (3).

Answer 9

e^6

Question 10

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

Answer 10

{y | y > 0}

Question 11

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

Answer 11

N^A+B

Question 12

Given f (x) = 3^x, evaluate f (4).

Answer 12

81

Question 13

What is the domain of the function

f (x) = 2^x?

Answer 13

{R}