A square root function is a function whose rule contains a variable under a square root sign

Chapter 11-1 Square-Root Functions Part 1 A square root function is a function whose rule contains a variable under a square root sign. Example: Gr...
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Chapter 11-1

Square-Root Functions Part 1

A square root function is a function whose rule contains a variable under a square root sign.

Example: Graph the square-root function. Use a calculator to approximate y.

x 0 1 2 3 4

y

Example: Graph the square-root function. Use a calculator to approximate y.

x 0.5 1 2 3 4

y

Chapter 11-1 Domain of Square-Root Functions Part 2 The domain of a square root function is all x values that make the expression under the radical sign greater than or equal to 0.

Example: Find the domain of

Example: Find the domain of

.

.

Example: Find the domain and graph the square-root function. Use a calculator to approximate y.

x 3 4 5 6 7

y

Chapter 11-2 Simple Radical Form Part 1 A square root is in simple radical form when;  The square root contains no perfect square factors.  The square root contains no fractions.

Product Property of Square Roots:

How to Simplify a Radical Expression  Find the greatest perfect square factor.  Factor using the greatest perfect square factor.  Apply the product property of square roots to the radicand.  Simplify the perfect square factor.

Example: Simplify,

Example: Simplify,

Example: Simplify,

Example: Simplify,

Chapter 11-2 Square Roots with Variables Part 2 A square root is in simple radical form when;  The square root contains no perfect square factors.  The square root contains no fractions.  The square root contains no variables with even powers. Square Roots of Variables:

How to Simplify a Radical Expression  Find the greatest perfect square factor.  Factor using the greatest perfect square factor.  Apply the product property of square roots to the radicand.  Simplify the perfect square factor.  Simplify any variable expressions using the pattern above.

Example: Simplify,

Example: Simplify,

Example: Simplify,

Example: Simplify,

Chapter 11-3 Add and Subtract Square Roots Part 1 The symbol

is called a radical sign.

The expression under a radical sign is called the radicand. Square root expressions with the same radicand are called like radicals. Adding Like Radicals:

Example: Add,

Example: Add,

Example: Add,

Subtracting Like Radicals:

Example: Add,

Example: Add,

Example: Add,

Chapter 11-3 Add and Subtract Square Roots Part 2 How to add or subtract expressions with unlike radicals:  Write each square root in simple radical form.  Add or subtract the like radicals.

Example: Add,

Example: Add,

Example: Subtract,

Example: Add,

Example: Subtract,

Chapter 11-4

Multiply Square Roots Part 1

Product Property of Square Roots:

Example: Multiply,

Example: Multiply,

Example: Multiply,

Example: Multiply,

Example: Multiply,

Example: Multiply,

Chapter 11-4 Divide Square Roots Part 2 Quotient Property of Square Roots:

Example: Divide,

Example: Divide,

Example: Divide,

Example: Divide,

Example: Divide,

Chapter 11-5

Radical Equations Part 1

A radical equation is an equation that contains a variable within a radical. Power Property:

Example: Solve for x,

Example: Solve for x,

Example: Solve for x,

Example: Solve for x,

Example: Solve for x, 2

Chapter 11-5

Radical Equations Part 2

A radical equation is an equation that contains a variable within a radical. Power Property:

Example: Solve for x,

Example: Solve for x,

Example: Solve for x,

Example: Solve for x,

Chapter 11-6

Geometric Sequences Part 1

In a geometric sequence, the ratio of consecutive terms is the same number r, called the common ratio. Example: Find the common ratio for the geometric sequence. 5 , -10 , 20 , -40 , . . .

Example: Find the common ratio for the geometric sequence. 2 , 6 , 18 , 54 , . . .

The common ratio can be used to find successive terms in a geometric sequence.

Example: Find the next three terms in the geometric sequence. 3 , 6 , 12 , 24 , ___ , ___ , ___

Example: Find the next three terms in the geometric sequence. 400 , 200 , 100 , 50 , ___ , ___ , ___

Example: Find the next three terms in the geometric sequence. 32 , 48 , 72 , 108 , ___ , ___ , ___

Chapter 11-6

Geometric Sequences Part 2

The nth term of a geometric sequence is given by the formula

Example: Use the nth term to find the first three terms.

Example: Use the nth term to find the first three terms.

Example: Use the nth term formula to find the 8th term of the geometric sequence. 2 , 20 , 200 , 2000 , . . .

Example: Use the nth term formula to find the 9th term of the geometric sequence. 8 , -16 , 32 , -64 , . . .

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