Understanding Rational Expressions and Domains

The video tutorial explains how to determine the values that make rational expressions undefined by setting the denominator to zero. It covers the concept of domain, which includes all real numbers except those that make the expression undefined. The tutorial provides three examples, each focusing on a different variable (X, Y, and Z), and demonstrates how to find the domain for each expression. It also discusses the importance of domain in defining functions and highlights the differences between similar expressions with different domains.

What makes a rational expression undefined?

• When the expression is negative

• When both numerator and denominator are zero

• When the denominator is zero

• When the numerator is zero

What is the domain of a rational expression?

• Only positive numbers

• All real numbers

• All numbers except those that make the numerator zero

• All numbers except those that make the denominator zero

For the expression 6 - x, what value of x makes it undefined?

• x = 6

• x = -6

• x = 1

• x = 0

What is the domain of the expression 3y / (y^2 - 16)?

• All real numbers except 16

• All real numbers except 0

• All real numbers except 4 and -4

• All real numbers

Which values of z make the expression z^2 + 5z + 6 undefined?

• z = -1 and z = -4

• z = 2 and z = 3

• z = -2 and z = -3

• z = 0 and z = 1

What is the domain of the expression z^2 + 5z + 6?

• All real numbers

• All real numbers except 0

• All real numbers except 2 and 3

• All real numbers except -2 and -3

Why can't you cancel out z + 3 in the expression (z + 3) / (z + 2)(z + 3)?

• Because it changes the numerator

• Because it changes the denominator

• Because it changes the domain

• Because it changes the expression to zero

What happens if you don't restrict the domain when simplifying expressions?

• The expression becomes negative

• The expression becomes zero

• The expression becomes undefined

• The expression remains the same

What is the result of factoring z^2 + 5z + 6?

• (z + 2)(z + 3)

• (z - 2)(z - 3)

• (z + 1)(z + 6)

• (z + 3)(z + 4)

What is the importance of understanding the domain in rational expressions?

• To simplify the expression

• To solve for x

• To identify undefined values

• To find the range