Understanding Reciprocal Functions

This video tutorial explains how to find the domain and range of reciprocal functions. It covers the standard form of reciprocal functions, how to sketch them using horizontal and vertical asymptotes, and how to determine the domain and range by excluding these asymptotes. The video also provides additional resources and examples to reinforce learning.

What is the standard form of a reciprocal function?

• y = a(x - h) + k

• y = a / x + h + k

• y = a / (x - h) + k

• y = ax + b

In the example given, what is the horizontal asymptote of the function y = a / (x - h) + k?

• x = k

• y = h

• x = h

• y = k

When sketching the graph of a reciprocal function, which quadrants will the graph be in if 'a' is positive?

• Quadrants 1 and 3

• Quadrants 2 and 3

• Quadrants 2 and 4

• Quadrants 1 and 2

What must be excluded from the domain of a reciprocal function?

• Neither asymptote

• Both asymptotes

• Vertical asymptote

• Horizontal asymptote

What is the range of a reciprocal function if the horizontal asymptote is y = 4?

• (-∞, 4]

• (-∞, 4) ∪ (4, ∞)

• (-∞, ∞)

• [4, ∞)

What additional content is available for students interested in learning more about reciprocal functions?

• Only physics

• Math and science playlists

• Only calculus

• Only algebra

For the function y = 5 / (x + 1) + 2, what is the vertical asymptote?

• y = 2

• y = -1

• x = -1

• x = 1

In the function y = 5 / (x + 1) + 2, what is the horizontal asymptote?

• x = -1

• y = 2

• x = 2

• y = 1

If 'a' is negative in a reciprocal function, which quadrants will the graph occupy?

• Quadrants 1 and 2

• Quadrants 3 and 4

• Quadrants 2 and 4

• Quadrants 1 and 3

What is the domain of the function y = 5 / (x + 1) + 2?

• (-∞, -1) ∪ (-1, ∞)

• (-∞, 1) ∪ (1, ∞)

• (-∞, 2) ∪ (2, ∞)

• (-∞, 0) ∪ (0, ∞)