Reciprocal Functions and Their Properties

This video tutorial covers the reciprocal function family, focusing on graphing inverse variations and their transformations. It explains the general form of reciprocal functions, including asymptotes, and provides a step-by-step guide to graphing these functions. The tutorial also discusses the domain and range, and how to perform transformations such as dilation and reflection. By the end of the lesson, students should be able to graph reciprocal functions and apply transformations using the general form.

What is the main objective of the lesson on reciprocal functions?

• To explore the history of algebra

• To learn how to solve quadratic equations

• To graph inverse variations and their transformations

• To understand the properties of linear functions

What is the general form of a reciprocal function?

• y = a^x

• y = a/(x-h) + k

• y = ax^2 + bx + c

• y = mx + b

Why can't x equal h in the general form of a reciprocal function?

• Because it would make the function undefined

• Because it would make the function linear

• Because it would make the function constant

• Because it would make the function quadratic

What are the asymptotes of the parent reciprocal function y = 1/x?

• x = 0 and y = 0

• x = 1 and y = 1

• x = -1 and y = -1

• x = 2 and y = 2

In which quadrants do the branches of the parent reciprocal function y = 1/x lie?

• First and third

• Second and third

• Third and fourth

• First and second

What is the domain of the function y = 12/x?

• All real numbers except x = 0

• All real numbers except x = 12

• All real numbers except x = -12

• All real numbers except x = 1

What happens to the graph of y = a/x when a is less than 1 but greater than 0?

• It shifts to the right

• It shrinks towards the origin

• It enlarges away from the origin

• It shifts to the left

How does the graph of y = a/x change when a is negative?

• It reflects over the x-axis

• It shifts downwards

• It reflects over the y-axis

• It shifts upwards

What is the effect of adding a constant k to the reciprocal function y = a/(x-h) + k?

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

• It shifts the graph vertically

• It shifts the graph horizontally

If the reciprocal function is y = 1/(x+1) - 4, in which direction is the graph shifted?

• Right 1 unit and up 4 units

• Left 1 unit and down 4 units

• Right 1 unit and down 4 units

• Left 1 unit and up 4 units