Understanding Rational Functions

The video tutorial explains how to determine the domain of a rational function, specifically f(x) = 2/(x + 2). It highlights the importance of identifying values that make the denominator zero, leading to undefined points and vertical asymptotes. The tutorial guides viewers through creating a table of values, performing substitutions, and plotting points to graph the function. It also discusses the presence of horizontal asymptotes and concludes with a comprehensive graph analysis.

What is the domain of the function F(x) = 2/(x + 2)?

• All real numbers

• All real numbers except x = -2

• All positive numbers

• All negative numbers

What happens to the graph of a function at a vertical asymptote?

• It reflects over the asymptote

• It becomes undefined

• It approaches but never crosses the asymptote

• It crosses the asymptote

Why is it important to include x = -2 in the middle of the table of values?

• To find the maximum value

• To ensure symmetry

• To highlight where the function is undefined

• To simplify calculations

What is the y-value when x = 0 for the function F(x) = 2/(x + 2)?

• Undefined

• 1

• 0

• 2

How do you calculate the y-value for x = -1.5 in the function F(x) = 2/(x + 2)?

• 2 multiplied by -0.5

• 2 divided by 0.5

• 2 multiplied by 0.5

• 2 divided by -0.5

What is the y-value when x = -3 for the function F(x) = 2/(x + 2)?

• -1

• -2

• -3

• 0

What is the significance of a horizontal asymptote in a rational function?

• It is where the function has a maximum value

• It shows the end behavior of the function

• It indicates where the function is undefined

• It is where the function has a minimum value

As x approaches positive infinity, what does the function F(x) = 2/(x + 2) approach?

• Infinity

• 0

• 1

• 2

What is the horizontal asymptote of the function F(x) = 2/(x + 2)?

• y = 0

• y = 2

• y = -2

• y = 1

What happens to the function F(x) = 2/(x + 2) as x approaches negative infinity?

• It approaches 0

• It approaches negative infinity

• It approaches 2

• It approaches 1