AP Calculus AB: 5.2.1 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.

• 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.

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.

2

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.

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.

1

1/2

e^6

{y | y > 0}

N^A+B

81

{R}