Embedded Files
Determine the Restrictions of a Radical Expression
You are asked to find the points where the radicand is greater than or equal to zero.
The Zero Method
Precalculus and calculus have unique ways of graphing a function without using a grapher.
In this course, the grapher will be used in other ways, not to see the behavior of a function.
There are several methods we will use to determine the function's behavior.
This will be done using the Zero Method.
Determining the behavior of the function
Precalculus - Zero Method
We will use the zero method to determine the function's behavior. This includes finding the factors of the polynomial and setting these factors equal to zero.
Example 5: Algebraic Solution
~ Determining the restriction(s) for radical expressions involves a bit more analysis than finding the rational restrictions.
~ Keep in mind that the radicand (the expression under the radical sign) must be greater than or equal to 0.
~ Because of the "greater than," we need to do more than identify the zeros.
~ The analysis involves looking at the behavior around the zeros.
We will use the process explained in the last presentation.
~ To do this, we need to include test points to determine whether the result around the zeros is (in this case) positive.
~ Look over the example below to understand the process used to determine the restrictions for radical equations.
~ Again, take the time and effort to understand the process as it will be used throughout this course and more so in Calculus.
Example 5: Graph Solution
The graph below shows why all values greater than 0 (also including x = -4 and x = 4) will satisfy the radicand's restrictions.
Note: These are not vertical asymptotes.
Google Sites
Report abuse