Understanding Domains of Logarithmic Functions

The video tutorial explains how to find the domain of logarithmic functions using inequalities and interval notation. It covers two examples: one with a log base 2 function and another with a common log (base 10) function. The process involves solving inequalities to determine the domain and expressing it in interval notation. The tutorial also includes graphing techniques to visualize the domain.

What is the first step in finding the domain of a logarithmic function?

• Convert the logarithm to exponential form

• Set the base of the logarithm to zero

• Integrate the function

• Find the derivative of the function

For the function y = log base 2 of (2x - 4), what inequality must be solved to find the domain?

• 2x - 4 ≤ 0

• 2x - 4 < 0

• 2x - 4 = 0

• 2x - 4 > 0

How is the domain of y = log base 2 of (2x - 4) expressed in interval notation?

• (2, ∞)

• [2, ∞)

• (-∞, 2)

• (-∞, 2]

What is the base of a common logarithm?

• 2

• e

• 10

• 1

Which inequality represents the domain of the function x^2 - 3x in the second example?

• x^2 - 3x ≤ 0

• x^2 - 3x = 0

• x^2 - 3x > 0

• x^2 - 3x < 0

What are the solutions to the equation x(x - 3) = 0?

• x = -3 and x = 3

• x = 1 and x = 3

• x = 0 and x = 3

• x = 0 and x = -3

Which interval is part of the domain for x^2 - 3x > 0?

• (-∞, ∞)

• (3, ∞)

• (0, 3)

• (-∞, 0)

In interval notation, how is the domain of the function x^2 - 3x expressed?

• [0, 3]

• (-∞, 0) ∪ (3, ∞)

• (-∞, 3)

• (0, 3]

Why are the intervals for the domain of x^2 - 3x open?

• Because the inequality is strict

• Because the function is discrete

• Because the inequality is non-strict

• Because the function is continuous

What is the significance of testing values in different intervals for the inequality x^2 - 3x > 0?

• To determine which intervals satisfy the inequality

• To find the maximum value of the function

• To calculate the derivative of the function

• To integrate the function over the interval