Understanding 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 a vertical asymptote. The tutorial also covers plotting points and understanding function transformations, including shifts.

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

• All negative numbers

• All positive numbers

• All real numbers except x = 2

• All real numbers

Why is x = 2 excluded from the domain of the function?

• Because it makes the numerator zero

• Because it makes the denominator zero

• Because it makes the function negative

• Because it makes the function positive

What is a vertical asymptote in the context of this function?

• A horizontal line the graph approaches

• A vertical line the graph approaches

• A point where the graph crosses the x-axis

• A point where the graph crosses the y-axis

What happens to the function at x = 2?

• The function is defined

• The function is zero

• The function is undefined

• The function is infinite

When x = 4, what is the value of the function f(x) = 1/(x-2) + 1?

• 0.5

• 3

• 1.5

• 2

What is the y-value when x = 1.5 for the function f(x) = 1/(x-2) + 1?

• -1

• 0

• 1

• 2

What does the graph of the function do as it approaches the vertical asymptote?

• It crosses the asymptote

• It approaches but never touches the asymptote

• It becomes horizontal

• It becomes a straight line

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

• y = 2

• y = 1

• y = -1

• y = 0

How is the function f(x) = 1/(x-2) + 1 related to the basic rational function y = 1/x?

• It is shifted down one unit and left two units

• It is shifted up one unit and right two units

• It is shifted down one unit and right two units

• It is shifted up one unit and left two units

What transformation occurs to the graph of y = 1/x to obtain the graph of f(x) = 1/(x-2) + 1?

• Shifted up one unit and left two units

• Shifted down one unit and right two units

• Shifted up one unit and right two units

• Shifted down one unit and left two units