Rational Functions: Domain and Range

The video tutorial introduces rational functions, explaining how to find their domain and range. It provides examples, such as f(x) = 1/(x-2) and x+5 over 3x^2-6x, to illustrate the process of determining the domain by setting the denominator not equal to zero. The tutorial also covers finding the range by graph analysis and algebraic manipulation. The video concludes with a summary and an invitation for questions.

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

• All real numbers except x = 2

• All real numbers except x = -2

• All real numbers

• All real numbers except x = 0

Why is the domain of a rational function restricted?

• Because the numerator cannot be zero

• Because the function is only defined for negative numbers

• Because the function is undefined when the denominator is zero

• Because the function is only defined for positive numbers

What values of x make the denominator zero in the function f(x) = (x+5)/(3x^2-6x)?

• x = 2 and x = 3

• x = 1 and x = 3

• x = 0 and x = 2

• x = -5 and x = 6

What is the domain of the function f(x) = (x+5)/(3x^2-6x)?

• All real numbers except x = 2 and x = 3

• All real numbers except x = -5 and x = 6

• All real numbers except x = 1 and x = 3

• All real numbers except x = 0 and x = 2

How can the range of a rational function be determined?

• By setting the numerator equal to zero

• By setting the denominator equal to zero

• By graphing the function or solving for x in terms of y

• By finding the x-intercepts

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

• All real numbers except y = 2

• All real numbers

• All real numbers except y = 0

• All real numbers except y = 1

What is the domain of a rational function based on its graph?

• All y-values where the graph is discontinuous

• All y-values where the graph is continuous

• All x-values where the graph is discontinuous

• All x-values where the graph is continuous

What is the range of a rational function based on its graph?

• All y-values where the graph is discontinuous

• All x-values where the graph is continuous

• All y-values where the graph is continuous

• All x-values where the graph is discontinuous

In the graph of a rational function, what does a vertical line test help determine?

• The x-intercepts of the function

• The range of the function

• The y-intercepts of the function

• The domain of the function

In the graph of a rational function, what does a horizontal line test help determine?

• The x-intercepts of the function

• The y-intercepts of the function

• The domain of the function

• The range of the function