1.3 and 1.4 January 6, 2010

1.1 p #2-12 even, even 2) rational, real 4) natural, integer, rational, real 6) Rational, real 8) integer, rational, real

1.1 continued 10) 3/1 (natural, integer, rational, real) -5/8 (rational, real) √7 (irrational, real).45… (rational, real) 0 (integer, rational, real) 5.6 x 10 3 (rational, real, integer, natural)

1.1 continued 12) -103 (integer, rational, real) 21/25 (rational, real) √100 = 10 (natural, integer, rational, real) -5.7/10 (rational, real) 2/9 (rational, real) (rational, real) √3 (irrational, real)

even, even 20) % 22) -4.9% 24) x ) x ) x ) x ) 1.25 x ) 7 x ) 7.89 x ) 9 x 10 5, 900,000 54) 5.6 x 10 -1, ) 6.25 x 10 -4, ) 3 x 10 2, ) 4.1 x 10 4, 41,000 62) 5 x 10 1, 50 64) 3.36 x 10 19

52-78 even, even 66) 5 x ) 3.78 x ) ) ) ) ) ) 102,000 86) The Amazon river discharges more than 1 cubic mile per day 88) cm 90) a) military decreased between 1975 and 2002, with a slight increase between , and it held steady between b) 2.6 million in 1975, 1.4 million in 2001

1.2 (p. 25) #5-12 all, all, all, all 5) a) max: 61, min: -30 b) mean: 136/9= 15.1 Median: 15, range: 91 6) a) max: 4.75, min: -3.5 b) mean: 10.25/7=1.46 Median: 1.5, range: ) a) max: π 2, min: √15 b) mean: 5.95 Median: 4.51, range: ) a) max: 3 1.2, min: 3 √28 b) mean: 3.27 Median: 3.14, range: ) a) S={ (-1,5), (2, 2), (3, -1), (5, -4), (9, -5) b) D= {-1, 2, 3, 5, 9) R= {5, 2, -1, -4, -5)

1.2 (p. 25) #5-12 all, all, all, all 10) a) S= {(-2, -4), (0, -2), (2, -1), (4, 0), (6, 4)} b) D= {-2, 0, 2, 4, 6) R= {-4, -2, -1, 0, 4} 11) a) S= {(1, 5), (4, 5), (5, 6), (4, 6), (1, 5)} b) D= {1, 4, 5} R= {5, 6} 12) a) S= {(-1, ½), (0, 1), (3, ¾), (-1, 3), (-2, - 5/6 ) b) D= {-2, -1, 0, 3}

1.2 (p. 25) #5-12 all, all, all, all 21) 522) 13 23) √29 = ) √50= ) √133.37= ) √41.49= ) 8 28) 8 43) years 44) 1,082,905 inmates 45) 543,949 minutes 46) 207 million 47) 10 second 48) (a+b)/2

1.2 (p. 25) #5-12 all, all, all, all 61) D= {-3, -2, 0, 7) R= {-5, -3, 0, 4, 5} 62) D={-5, 0, 1, 3, 8} R= {-5, -2, 0, 1, 3} 63) D= {-4, -3, -1, 0, 2) R= {-2, -1, 1, 2, 3} 64) D= {-1, 1, 2} R= {-3, -1, 0, 1, 2} 65) D= {-35, -25, 0, 10, 75} R= {-55, -25, 25, 45, 50} 66) D= {-17, -7, -5, 2, 11} R= {-14, -13, -4, 15, 19} 67) D= {-0.7,0.1, 0.5, 0.8} R= {-0.3, -0.1, 0, 0.4} 68) D= {-1.2, -0.8, -0.3, 1.0} R= {-1.3, 0.5, 1.1, 1.5}

Objectives Learn function notation Represent a function four different ways Identify the range and domain of a function Identify functions

What is a function? A function is a relation in which every input (x) has exactly one output (y). To emphasize that y is a function of x, the notation y=f(x) is often used. The variable y is called the dependent variable. The variable x is called the independent variable.

Anatomy of a function y= f(x) f(20)=4 would read.. …f of 20 equals 4 f, g, and h are often used as names of functions. output name input

Domain and range The set of valid or meaningful inputs (x) is called the domain of a function. The corresponding outputs (y) is the range. Examine f(x)=x 2. – What would be the domain? – What would be the range Unless stated otherwise, the domain of a function f is the set of all real numbers that make sense for the function. This is called the implied domain.

Formal definition of a function A function is a relation in which each element in the domain corresponds to one element in the range.

The vertical line test If every possible vertical line intersects a graph at no more than one point, then the graph represents a function. Do these pass?

Representations of functions Verbally: in words Numerically: table of values – Since it is often not possible or appropriate to list all values, this type of table is often referred to as a partial numerical representation Symbolically: formula Graphically: graph

Using these representations Symbolic: f(x)=x+1 Numerically Graphically Verbally

Find the domain of function f f(x) =x 2 -4 x-2

Try this Find the domain and range. Evaluate f(0) and f(2) Find all x such that f(x)= -1

1.4: Types of Functions and their Rates of Change

Objectives Identify and use constant and linear functions. Interpret slope as a rate of change. Identify and use non-linear functions. Recognize linear and non-linear data. Use and interpret average rate of change.

Constant Function A constant function is represented by: f(x)=b where b is a constant (fixed) number. Examples include: f(x)=10 f(x)= ½ What would the graph of a constant function look like?

Linear Function A linear function is represented by: f(x)=ax+b where a and b are constant (fixed) numbers. You may have also have seen this as y=mx+b. What would the graph of a linear function look like?

Slope Slope = m = y 2 -y 1 x 2 -x 1 Slope is also called rate of change. What is the slope of this graph?

Linear vs. nonlinear These are examples of nonlinear graphs. Notice that none of them are straight lines.

Average rate of change To find the average rate of change between two point, use the formula for slope. Plug in the two coordinates as x 1, x 2, y 1, and y 2.

Find the average rate of Find the average rate of change between 0 and 4 for each graph.

Your assignment 1.3Page #20-50 #53-58 # , p. 58 #1-16, 25-30, 65-67, 75-78