Exploring Domain and Range of Rational Expressions

This video tutorial by Mark Kara Demos on mathguide.com covers three examples of rational expressions. It explains how to find horizontal and vertical asymptotes, and how to determine the domain and range of these expressions. The video provides step-by-step instructions and diagrams to illustrate the concepts, helping viewers understand the relationship between algebraic calculations and graphical representations.

How do you find a vertical asymptote of a rational expression?

• Divide the leading coefficients

• Set the denominator equal to zero

• Set the numerator equal to zero

• Compare the degrees of the numerator and denominator

What is the horizontal asymptote if the degree of the denominator is greater than the numerator?

• y = 0

• y = 1

• No horizontal asymptote

• x = 0

How is the domain of a rational function with a vertical asymptote at x = 5 represented?

• x ≠ 5

• x > 5

• x < 5

• All real numbers

What is the range of a function approaching y = 0 but never touching it?

• y < 0

• y > 0

• y = 0

• All real numbers except y = 0

In the second example, how many vertical asymptotes are identified?

• One

• Two

• None

• Three

What is the horizontal asymptote when the numerator's degree is 0 and the denominator's degree is 2?

• x = 0

• y = 1

• y = 0

• No horizontal asymptote

For the final example, what is the horizontal asymptote when both degrees are equal?

• No horizontal asymptote

• x = 4

• y = 4

• y = 0

What determines the domain of a rational function?

• The leading coefficients of the expression

• Values that make the numerator zero

• Values that make the denominator zero

• The highest degree of the expression

How is the range of a function determined?

• By dividing the leading coefficients

• By setting the denominator to zero

• By analyzing the graph's behavior

• By comparing the degrees of numerator and denominator

What is the vertical asymptote of the function 4x + 3 over x - 2?

• x = 4

• x = 3

• x = -2

• x = 2