Understanding Rational Functions

The video tutorial explains how to analyze a rational function, focusing on finding the domain, vertical and horizontal asymptotes, and the range. It uses a graphing calculator to visualize the function and verify the findings. The domain excludes values that make the denominator zero, while vertical asymptotes occur at these points unless the numerator is also zero. Horizontal asymptotes are determined by the behavior of the function as x approaches infinity. The range excludes the horizontal asymptote value. The tutorial concludes with graphing the function and summarizing the key points.

What is the domain of the function f(x) = 1/(x - 2) + 4?

• All real numbers except x = 0

• All real numbers except x = 4

• All real numbers except x = 2

• All real numbers

Why is x = 2 not included in the domain of the function?

• Because it makes the function undefined

• Because it makes the function equal to zero

• Because it makes the denominator zero

• Because it makes the numerator zero

What is the vertical asymptote of the function f(x) = 1/(x - 2) + 4?

• x = -2

• x = 4

• x = 2

• x = 0

How can you verify the vertical asymptote using a graphing calculator?

• By checking if the graph crosses the x-axis

• By checking if the graph has a break at x = 2

• By checking if the graph crosses the y-axis

• By checking if the graph is continuous

What happens to the function value as x approaches infinity?

• It approaches infinity

• It approaches 4

• It approaches 2

• It approaches 0

What is the horizontal asymptote of the function f(x) = 1/(x - 2) + 4?

• y = -4

• y = 4

• y = 0

• y = 2

Why does the function never reach the value of 4?

• Because the denominator is a constant

• Because the numerator is a constant

• Because the denominator is zero

• Because the numerator is zero

What is the range of the function f(x) = 1/(x - 2) + 4?

• All real numbers

• All real numbers except y = 0

• All real numbers except y = 4

• All real numbers except y = 2

How does the function behave as x approaches negative infinity?

• It approaches 4

• It approaches 0

• It approaches negative infinity

• It approaches 2

What is the significance of the horizontal asymptote in the graph of the function?

• It indicates where the graph crosses the x-axis

• It indicates the value the function approaches as x goes to infinity

• It indicates where the graph crosses the y-axis

• It indicates the maximum value of the function