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 function. The process involves solving inequalities to determine the domain and expressing it in interval notation. The tutorial also demonstrates how to use a number line to test intervals for a quadratic inequality.

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

• Determine the base

• Find the range

• Solve the inequality

• Graph the function

In the first example, what inequality must be solved to find the domain?

• 2x + 4 > 0

• x^2 - 3x > 0

• 2x - 4 > 0

• x + 3 > 0

How is the domain expressed in interval notation for the first example?

• (0, 2)

• (2, ∞)

• [2, ∞)

• (-∞, 2)

What is the base of the logarithm in the second example?

• e

• 2

• 10

• 5

What type of inequality is solved in the second example?

• Rational inequality

• Exponential inequality

• Quadratic inequality

• Linear inequality

Which values of x make the expression x^2 - 3x equal to zero?

• x = 1 and x = 3

• x = 0 and x = 1

• x = 0 and x = 3

• x = -1 and x = 3

What is the domain of the second function using inequalities?

• x < 0 and x > 3

• x < 0 or x > 3

• x > 0 and x < 3

• x > 0 or x < 3

In interval notation, how is the domain of the second function expressed?

• (-∞, 3) ∪ (0, ∞)

• [0, 3]

• (0, 3)

• (-∞, 0) ∪ (3, ∞)

Why are open intervals used in the domain of the second function?

• Because the endpoints are included

• Because the endpoints are not included

• Because the function is continuous

• Because the function is discrete

What is the main takeaway from the video regarding logarithmic functions?

• The domain of logarithmic functions is always all real numbers

• Logarithmic functions have no domain

• Logarithmic functions are always increasing

• The domain of logarithmic functions is determined by the inequality of the argument