Understanding Domains of Rational Functions

The video tutorial explains how to determine the domain of rational functions by identifying values that make the denominator zero, thus excluding them from the domain. It provides three examples, each demonstrating different methods to solve for excluded values, including solving linear and quadratic equations. The tutorial also discusses the importance of not simplifying rational functions before determining the domain, as simplification can affect the domain by removing necessary factors.

What is the first step in determining the domain of a rational function?

• Set the denominator equal to zero

• Find the range of the function

• Graph the function

• Set the numerator equal to zero

In the first example, what value of X is excluded from the domain?

• X = 5 1/2

• X = -5

• X = 5

• X = 0

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

• (-∞, 5 1/2) ∪ (5 1/2, ∞)

• (-∞, 5) ∪ (5, ∞)

• (-∞, 0) ∪ (0, ∞)

• (-∞, 5 1/2)

What is the greatest common factor in the second example?

• X^2

• 3

• X

• 2

Which values are excluded from the domain in the second example?

• X = -3 1/2 and X = 3

• X = 0 and X = 3

• X = 0 and X = -3 1/2

• X = 0 and X = 5

In the third example, what are the solutions to the equation X^2 + 4X - 21 = 0?

• X = 7 and X = -3

• X = -7 and X = 3

• X = -7 and X = -3

• X = 7 and X = 3

How is the domain expressed using interval notation for the third example?

• (-∞, 3) ∪ (3, 7) ∪ (7, ∞)

• (-∞, -7) ∪ (-7, 3) ∪ (3, ∞)

• (-∞, -7) ∪ (-7, 0) ∪ (0, ∞)

• (-∞, -3) ∪ (-3, 7) ∪ (7, ∞)

Why should we not simplify rational functions before determining the domain?

• It makes the calculations more complex

• It affects the numerator

• It can lead to incorrect domain exclusions

• It is unnecessary for graphing

What does a common factor in the numerator and denominator produce in the graph of a rational function?

• A vertical asymptote

• A hole

• A zero

• A horizontal asymptote

What is the effect of a zero in the denominator on the graph of a rational function?

• It creates a hole

• It creates a zero

• It creates a vertical asymptote

• It creates a horizontal asymptote