EET 109 Math January 26, 2016 Week 4 Day 1

Average score = 88.4%

Home work: A railroad track has an angle of elevation of 1.0°. What is the difference in altitudes of two points on the track which are (a) 1.00 mi apart and (b) 1.00 km apart?

Home work: If the span of the bridge in Exercise 7 is to be 16.0 m above the roadway and the angle of elevation of the approach is to be 5.0°, how long will the approach be?

Is the plane flying in a straight line?

WEEK 4 Day 1

4.1 Functions 4.2 Graphing Equations 4.3 The Straight Line 4.4 Parallel and Perpendicular Lines 4.5 The Distance and Midpoint Formulas

Chapter 4 Equations and Their Graphs Functions and their equations can be graphed. This graphic representation, which connects algebra and geometry, is important in solving problems. Page 145

4.1 FUNCTIONS page 145 In mathematics a relation is defined as a set of ordered pairs of numbers in the form (x, y). As an equation that states the relationship between x and y.

4.1 FUNCTIONS page 145 In an ordered pair the first variable is called the independent variable. The second variable is called the dependent variable

4.1 FUNCTIONS page 146 The domain is often referred to as the set of all x’s (Inputs). The range is often referred to as the set of all y’s. (Outputs).

ordered pairs of numbers in the form x y Independent variableDependent variable InputsOutputs Domain Range

4.1 FUNCTIONS page 146 First element

4.1 FUNCTIONS page 146 A relation is a function when for each possible value of the first or independent variable X, there is only one corresponding value of the second or dependent variable Y. In brief, for a relation to be a function, each value of x must correspond to one, and only one, value of y. THAT VALUE MAY BE THE SAME FOR Y FOR DIFFERENT XS.

No

InputsOutputs Domain Range Outputs Variable Inputs Doman

4.1 FUNCTIONS page 147 Functional notation: Stated as: “f of x”

Y = f (x) This is f of X NOT f times x. Inputs Outputs

Y = f (x) X Y

4.2 GRAPHING EQUATIONS page 150 The point of intersection the zero point (0,0) of each line is called the origin. Each line is called an axis. The horizontal number line is usually called the x- axis and The vertical line is usually called the y-axis. Such a system is called the rectangular coordinate system, or the Cartesian coordinate system.

Page 151 Algebra and geometry together.

4.2 GRAPHING EQUATIONS page 152 Plotting points from order pairs.

Exercises 4.2 Home work 12 points Plotting is fundamental to correct graphs.

From (ordered) pairs to plotting points to graphing.

4.2 GRAPHING EQUATIONS PAGE 150 Doug’s tips for graphing a function. For X use -1, 0, 1, 2 The pair will be near the origin. The pair will allow for possible negative and positive outcomes. The numbers are mathematically easy to work with.

4.2 GRAPHING EQUATIONS page 152 x y -1, 0, 2,

Page 152 A linear equation with two unknowns is an equation of degree one in the form with a and b not both 0. Degree means no exponents.

Page 153 For a more complicated function, more ordered pairs are usually required to obtain a smooth curve.

4.2 GRAPHING EQUATIONS page 152 The graph of a linear equation is a straight line. Therefore, two ordered pairs are sufficient to graph it, since two points determine a straight line. However, finding a third point provides good insurance against a careless error.

4.2 GRAPHING EQUATIONS page 152 The graph of an equation that is not linear is usually a curve of some kind and requires several points to sketch a smooth curve.

4.2 GRAPHING EQUATIONS page 152

You cant turn in your calculator.

Graphing Calculator

Page 154 Solving for y = 0 This graphically means finding the point or points, if any, where the graph crosses the y axis. x y (0, 2)

Solving Equations by Graphing Equations may be solved graphically. This method is particularly useful when an algebraic method is very cumbersome, cannot be recalled, or does not exist; it is especially useful in technical applications.

1.7 EXPONENTS AND RADICALS

Y intercept may be solved graphically.

4.3 THE STRAIGHT LINE Page 162 Y intercept may be solved mathematically. (section 4.3)

4.3 THE STRAIGHT LINE Page 162

4.3 THE STRAIGHT LINE page 159 Analytic geometry is the study of the relationships between algebra and geometry. We now develop several basic relations between equations and their graphs.

4.3 THE STRAIGHT LINE page 159 The slope of a nonvertical line is the ratio of the difference of the y-coordinates of any two points on the line to the difference of their x- coordinates when the differences are taken in the same order.

4.3 THE STRAIGHT LINE page 159 The slope of a line.

Any 2 ordered pair can be used.

Rise over run is not in the text.

Split the ordered pairs: Don’t divide one pair by the other. Don’t have x - y by x - y

If a line has positive slope, then the line slopes upward from left to right (“rises”). If a line has negative slope, then the line slopes downward from left to right(“falls”).

If the line has zero slope, then the line is horizontal (“flat”).

If the line is vertical, then the line has undefined slope because of 0.

Where are we going? Where we have been.