Exploring Graphing Rational Functions

The video tutorial explains how to determine the domain of a rational function, complete a table of values, and graph the function. It highlights the importance of excluding values that make the denominator zero, leading to vertical asymptotes. The tutorial also covers horizontal asymptotes and transformations, providing a comprehensive understanding of graphing rational functions.

What is the domain of the function f(x) = 1 / (x - 2) + 1?

• All negative real numbers

• All real numbers

• All real numbers except x = 2

• All positive real numbers

Why must we exclude x = 2 from the domain of the function?

• Because it makes the numerator zero

• Because it makes the function negative

• Because it makes the denominator zero

• Because it makes the function positive

What happens at x = 2 for the function f(x) = 1 / (x - 2) + 1?

• The function is zero

• There is a horizontal asymptote

• There is a vertical asymptote

• The function is undefined

Why is it helpful to place x = 2 in the middle of the table of values?

• To avoid positive values

• To avoid negative values

• To select values greater and less than 2

• To make calculations easier

What is the value of the function when x = 4?

• 3

• 1.5

• 2

• 0.5

What is the value of the function when x = 2.5?

• 1.5

• 2

• 4

• 3

What is the value of the function when x = 1?

• 2

• 0

• 1

• -1

What is the horizontal asymptote of the function f(x) = 1 / (x - 2) + 1?

• y = 0

• y = 1

• y = 2

• y = -1

How does the function behave as x approaches positive infinity?

• It approaches y = 0

• It approaches y = 1

• It approaches y = 2

• It approaches y = -1

How has the function g(x) = 1 / (x - 2) + 1 been transformed from the basic rational function y = 1/x?

• Shifted up one unit and left two units

• Shifted down one unit and right two units

• Shifted down one unit and left two units

• Shifted up one unit and right two units