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 , . . .