Properties of Exponential and Logarithmic Functions

This lesson focuses on graphing natural log and exponential functions with base e. It explains how to graph e^x - 2 + 3 by setting the exponent to zero and one, finding x and y values, and identifying the horizontal asymptote. The lesson also covers graphing ln(x - 1) + 2 by setting the inside part to zero, one, and e, finding x and y values, and identifying the vertical asymptote. The techniques for graphing regular log and exponential functions are applicable to natural log and e-based functions.

What is the base of the natural log function?

• 10

• 2

• 5

• e

When graphing e^(x-2) + 3, what is the horizontal asymptote?

• y = 3

• y = -2

• y = 2

• y = 0

What is the y-value when x = 2 for the function e^(x-2) + 3?

• 4

• 3

• 6

• 5

What is the domain of the function e^(x-2) + 3?

• x > 2

• x < 0

• All real numbers

• x > 0

For the function ln(x-1) + 2, what is the vertical asymptote?

• x = -1

• x = 2

• x = 1

• x = 0

What is the y-value when x = 2 for the function ln(x-1) + 2?

• 1

• 0

• 3

• 2

What is the range of the function ln(x-1) + 2?

• y > 2

• All real numbers

• y < 0

• y > 0

What is the domain of the function ln(x-1) + 2?

• x > 0

• x < 0

• x > 1

• x < 1

What is the approximate value of e used in calculations?

• 2.71

• 3.14

• 1.62

• 2.18

Which of the following is true about the graph of e^(x-2) + 3?

• It has a horizontal asymptote

• It has a vertical asymptote

• It is a linear function

• It is a quadratic function