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

Tags

CCSS.HSF-IF.C.7D

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

Tags

CCSS.HSF-IF.C.7D

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

Tags

CCSS.HSF-IF.C.7D

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

• Neither asymptote

• Both asymptotes

• Vertical asymptote

• Horizontal asymptote

Tags

CCSS.HSF-IF.C.7E

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

• (-∞, 4]

• (-∞, 4) ∪ (4, ∞)

• (-∞, ∞)

• [4, ∞)

Tags

CCSS.HSF-IF.C.7D

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

• Only physics

• Math and science playlists

• Only calculus

• Only algebra

Tags

CCSS.HSF-IF.C.7D

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

• y = 2

• y = -1

• x = -1

• x = 1

Tags

CCSS.HSF-IF.C.7D

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

• x = -1

• y = 2

• x = 2

• y = 1

Tags

CCSS.HSF-IF.C.7D

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, ∞)