Understanding Reciprocal Functions

The video tutorial explains reciprocal functions, focusing on their equations and properties. It covers how to identify vertical and horizontal asymptotes and the effects of the parameter 'a' on the graph's shape. The tutorial provides a step-by-step guide to graphing reciprocal functions, including plotting points for accuracy. Two examples are discussed, illustrating the process of graphing reciprocal functions and identifying key features like asymptotes and intercepts. The video also offers additional resources for further 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 + h + k

If 'a' is greater than 1 in a reciprocal function, what effect does it have on the graph?

• Horizontal stretch

• Horizontal shrink

• Vertical shrink

• Vertical stretch

In which quadrants does the graph of y = 1/x exist when 'a' is positive?

• Quadrants 3 and 4

• Quadrants 1 and 2

• Quadrants 2 and 4

• Quadrants 1 and 3

For the function y = 2/(x - 3) + 1, what is the vertical asymptote?

• x = 4

• x = 1

• x = 3

• x = 2

What is the horizontal asymptote for the function y = 2/(x - 3) + 1?

• y = 3

• y = 0

• y = 1

• y = 2

In the function y = -4/(x + 1) + 2, what is the effect of the negative sign in front of 'a'?

• The graph is shifted up

• The graph is shifted down

• The graph is reflected over the x-axis

• The graph is reflected over the y-axis

For the function y = -4/(x + 1) + 2, what is the vertical asymptote?

• x = 2

• x = 0

• x = 1

• x = -1

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

• y = 3

• y = 2

• y = 1

• y = 0

Which of the following points is on the graph of y = -4/(x + 1) + 2?

• (0, -2)

• (-2, 6)

• (2, 1)

• (1, 0)

Where can you find more resources on graphing rational functions?

• In the video title

• On the video thumbnail

• In the video comments

• In the video description