8/8/17 Warm Up Solve the inequality.  

8/10/17 Warm Up Identify the function. 1. 2. 3.

Relations & Functions Domain/Range Parent Functions

A relation is a set of ordered pairs.

Domain and Range The set of input values (x) for a relation is called the domain, and the set of output values (y) is called the range.

Function (vertical line test) a special type of relation in which each element of the domain is paired with exactly one element of the range.

Not a function: The relationship from number to letter is not a function because the domain value 2 is mapped to the range values A, B, and C. Function: The relationship from letter to number is a function because each letter in the domain is mapped to only one number in the range.

Families of Functions or Relations

Polynomial Functions

Constant Functions y = c Domain: Range:

Identity Function y = x Domain: Range:

Linear Functions   Domain: Range:

Quadratic Functions y = ax2 + bx + c Domain: Range:

Cubic Functions   Domain: Range:

Power Functions f(x) = axb Domain: Range:

Absolute Value Functions y = │x│+1 Domain: Range:

Step Functions and Greatest Integer Function y = [x] Domain: Range:

Square Root Functions Domain: Range:

Exponential Functions y = abx y = 3(2)x Domain: Range:

Logarithmic Functions y = ln x or y = log x Domain: Range:

Rational Functions or Domain: Range: Domain: Range:

Identify the Function and Find Its Domain and Range

Identify the Function and Find Its Domain and Range

Trig Functions

Sine Function f(x) = sin (x)

Cosine Function f(x) = cos (x)

Tangent Function f(x) = tan (x)

Cotangent Function f(x) = cot (x)

Secant Function f(x) = sec (x)

Cosecant Function f(x) = csc (x)

What do you know about the number system?

The Real Number System

Name the sets of numbers to which belongs. The bar over the 9 indicates that those digits repeat forever. Answer: rationals (Q) and reals (R) Example 2-1b

Name the sets of numbers to which belongs. lies between 2 and 3 so it is not a whole number. Answer: irrationals (I) and reals (R) Example 2-1c

Name the sets of numbers to which belongs. Answer: naturals (N), wholes (W), integers (Z), rationals (Q) and reals (R) Example 2-1d

Name the sets of numbers to which –23.3 belongs. Answer: rationals (Q) and reals (R) Example 2-1e

Name the sets of numbers to which each number belongs. a. d. e. 32.1 Answer: rationals (Q) and reals (R) Answer: rationals (Q) and reals (R) Answer: irrationals (I) and reals (R) Answer: naturals (N), wholes (W), integers (Z) rationals (Q) and reals (R) Answer: rationals (Q) and reals (R) Example 2-1f

Name the sets of numbers to which belongs. Answer: rationals (Q) and reals (R) Example 2-1a

Properties of Real Numbers

Name the property illustrated by . The Additive Inverse Property says that a number plus its opposite is 0. Answer: Additive Inverse Property Example 2-2a

Name the property illustrated by . The Distributive Property says that you multiply each term within the parentheses by the first number. Answer: Distributive Property Example 2-2b

Name the property illustrated by each equation. a. Answer: Identity Property of Addition Answer: Inverse Property of Multiplication Example 2-2c

Identify the additive inverse and multiplicative inverse for –7. Since –7 + 7 = 0, the additive inverse is 7. Since the multiplicative inverse is Answer: The additive inverse is 7, and the multiplicative inverse is Example 2-3a

Identify the additive inverse and multiplicative inverse for . Since the additive inverse is Since the multiplicative inverse is Answer: The additive inverse is and the multiplicative inverse is 3. Example 2-3b

Answer: additive: –5; multiplicative: Identify the additive inverse and multiplicative inverse for each number. a. 5 b. Answer: additive: –5; multiplicative: Answer: additive: multiplicative: Example 2-3c

Distributive Property Simplify Distributive Property Multiply. Commutative Property (+) Distributive Property Answer: Simplify. Example 2-5a

Simplify . Answer: Example 2-5b