Understanding the Basic Rational Function

This video tutorial explains how to graph the basic rational function f(x) = 1/x. It covers creating a table of values to understand the function's behavior, plotting points on a coordinate plane, and analyzing how the graph approaches the x and y axes. The tutorial also defines vertical and horizontal asymptotes and explains the domain and range of the function using interval notation.

What is the basic rational function discussed in this lesson?

• f(x) = x - 1

• f(x) = x^2

• f(x) = 1/x

• f(x) = x + 1

What happens to the function f(x) = 1/x when x equals zero?

• The function is zero

• The function is undefined

• The function is one

• The function is infinite

Which of the following points is on the graph of f(x) = 1/x?

• (2, 2)

• (1, 1)

• (0, 1)

• (1, 0)

As x approaches zero from the positive side, what happens to the function values of f(x) = 1/x?

• They approach zero

• They approach positive infinity

• They approach negative infinity

• They remain constant

What is the vertical asymptote of the function f(x) = 1/x?

• y = 1

• y = 0

• x = 1

• x = 0

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

• y = 1

• y = 0

• x = 1

• x = 0

How is the domain of f(x) = 1/x expressed in interval notation?

• (0, ∞)

• (-∞, 0) ∪ (0, ∞)

• [0, ∞)

• (-∞, ∞)

Which of the following is true about the range of f(x) = 1/x?

• It is only positive numbers

• It excludes zero

• It is all real numbers

• It includes zero

What is the definition of an asymptote?

• A point where the graph is undefined

• A point where the graph crosses the axis

• A line that the graph approaches but never touches

• A curve that the graph intersects

Using inequalities, how can the range of f(x) = 1/x be expressed?

• f(x) < 0 or f(x) > 0

• f(x) ≤ 0 or f(x) ≥ 0

• f(x) = 0

• f(x) > 0