Notes Graph Rad Reg.pdf

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Unit 3

Radical Part A: Features

of Radical Functions

Notes Radical Functions

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Power of a Power Property

(Power to a power you multiply)

Example:

Power of a Product Property

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So pattern continues to the nth root.

So all numbers can have a nth root.

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Examples The “nth Root” used n times

Find the

realnumber root

Examples The “nth Root” used n times

Find the

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So I can have negative root with what types of roots?

So I will have an imaginary roots with types of roots?

Try the following using a calculator…..

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Radical’s can be as a

fractional .

The value goes on the

of the fraction.

Note

An exponent can be turned into a root. Example:

7.

8.

9.

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10.

11.

12.

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13.

14.

15.

Example: Rewrite in radical form.

Simplify if possible.

16.

17.

18.

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Radical Definition

Key Concept Radical Functions

What is the inverse of a power?

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Determine the inverse of the

power function ?

Graph the power function and inverse

Key Concept: When you restrict the

of the power function to

values or

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Square Root Function Parent

Domain:

Range:

Xintercept: yintercept:

End Behavior: Right:

Left:

student.desmos.com

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What is the difference in the graph when a constant is

added outside the radical , or inside of the

radical, ?

a) b) c) d)

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General Form of Cubic Root Family

The value of k affects …………..

The value of h affects………….

The value of a affect………

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Transformation using function notation

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Domain

Example:

Graph the square root function and

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Example: The sketch the graph of the parent function

. Next sketch the graph of the transformed

parent function.

a.

b.

Examples using function notation transformations

Example: Describe how each graph represented by

would be transformed to create the graph represent by

.

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Write and equation for each function by transforming

the equation as described.

b. is translated to the right 8 units and up

2 units.

Determine the inverse of the

power function ?

_{Graph the power function}

and inverse

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What is the difference in the graph when a constant is

added outside the radical , or inside of the

radical, ?

Graph the Following Functions on the Same Graph, each in a different color

a) b) c) d)

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General Form of Cubic Root Family The value of k affects ………….. The value of h affects…………. The value of a affect……… The value of b affect……… Transformation using function notation

If transformation notation looks like , how effect parent function?

If transformation notation looks like , how

effect parent function?

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Domain

Range

Example:

determine the domain and range.

Domain

Example:

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Example: The sketch the graph of the parent function

. Next sketch the graph of the transformed

parent function.

a.

b.

Examples using function notation transformations

Example: Describe how each graph represented by

would be transformed to create the graph represent by

.

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Write and equation for each function by transforming

the equation as described.

b. is translated to the Left 6 units and

down 3 units.

Unit 3

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Solve the following equations.

Example 1:

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Example 3:

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Example 5:

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Example 10:

In medicine, Body Surface Area BSA is used to help determine proper dosage for medications. The equation

models the relationship between BSA in square meters, the patient’s weight W in kilograms, and the patient’s height H in centimeters. Determine the height of a patient who weighs 90 kilograms and has a BSA of 2.1.

Big Ben is the nickname of a wellknown clock tower in London, England that stands 316 feet tall. The clock is driven by a 660 pound pendulum in the tower that continually swings back and forth. The relationship between the length of pendulum L in feet and the time it takes for a pendulum to swing back and forth on time, or its period T, is modeled by the equation

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Consider the radical equation shown.

What is the solution set to this equation?

a)

b)

c)

d)

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Example 7:

Solving Radical with x on both side (Graphically

and Algebraically)

Example 8:

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Example 9:

Solving Radical with x on both side (Graphically

and Algebraically)

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Solving Radical Equations with rational exponents

Step 1: Isolate the base with the rational exponent

Step 2: Get rid of the rational exponent

Step 3: Solve the remaining equation

Step 4: Check for extraneous solutions

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Example 2:

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