At the end of this lesson, you, as a successful student, will be able to understand and to use in activities
At the end of this session you will be able to
INCREMENT, delta X
You notice at the bottom of on page 1 of your textbook, a Greek letter delta is used for increment. Delta x represents x2 - x1 and delta y represented y2 - y1. Later in the textbook, you will see the letter "h" used to represent delta x = x2 - x1. In the same way, some textbooks use "k" for delta y.
SLOPE
You need to make sure that you know the definition of slope in the box on page 10 of your textbook.
CALCULATING SLOPE
You want to make sure that you practice calculating slope in Example 3 on page 11 without looking at the textbook.
CHOOSING POINT P1 AND POINT P2 FOR CALCULATING SLOPE
On page 10 of your textbook, some of you may question which point is used for P1 and which is used for P2. The answer is it does not matter. What does matter is that both the x-values and y-values are subtracted in the same direction. For example, in Example 3 at the bottom of page 11 in your textbook, you will have m = 1 if you also subtract (-1 - 4)/(-2 - 3).
You can now go to the Session 2 assignments to continue your assignment.
At the end of this session you will be able to
SLOPE-INTERCEPT FORM
Make sure that you know the definition of the slope-intercept form of a linear equation, y = mx + b, found at the top of page 12 of your textbook.
The slope-intercept form of the equation of a line is important because it is the form we use when entering a linear equation into our graphing calculator.
You may have learned to use the slope-intercept form to write an equation of a line. The following is how to do Example 2 on page 11 using the slope-intercept form:
Substitute x = 2, y = 3, and m = - 3/ 2 into the slope-intercept form. What do you have after substituting?
Solve this equation for b. What is the solution?
Now write your equation.
GENERAL FORM
Make sure you know the definition of the general form of a linear equation, Ax + By = C found in the middle of page 12 of your textbook. When you see an equation written in this form you are to recognize that geometrically you have a graph that is a straight line.
CONVERTING TO SLOPE-INTERCEPT FORM
Example 4 in the middle of page 12 illustrates how you convert an equation from general form into slope-intercept form, which allows you to then entering the equation into your graphing calculator.
Practice on your own paper going through the steps shown in the middle of pagte 12, but without looking at your textbook. Then enter the resulting slope-intercept form into your calculator. What does the graph look like?
You can now go to the Session 2 assignments to continue your assignment.
At the end of this session you will be able to
DEFINITION OF FUNCTION
Make sure that you know the definition of a function that is in the box near the bottom of page 19 and you study well the discussion on pages 19 and 20 of your textbook. You should know this material so well that you could describe the concept to someone else. Can you? If not then study it more.
DOMAIN and RANGE OF A FUNCTION
Insure that you know what is meant by the domain and range of a function as described at the bottom of page 19 of your textbook. Notice that the independent variable is a symbol for anything found in the domain and the dependent variable is a symbol for anything found in the range.
Also, study well page 20 of your textbook and the top of page 21 for an excellent discussion of domain and range. You want to make sure that you understand all of Example 1 at the bottom of page 20.
WAYS OF REPRESENTING A FUNCTION
Now that you have reviewed the concept of a function and it's graph, we will clarify some potential confusing areas for you.
There are four ways of representing functions:
- Verbally, by description in words. For example, the functional value P(t) is the United States population at time t.
- Numerically, by a table of ordered pairs. On page 23 of your textbook, the discussion and Table 12 illustrates functions represented numerically. The Table Function on your calculator is another way that we represent functions with tables.
- Algebraically, by an explicit formula. For example, we might represent a linear function by the rule f(x) = 3 x + 5.
- Visually, by a graph. In algebra, you graphed by plotting points on a coordinate plane. Of course, your graphing calculator is a quick way to obtain the graph.
INCREASING AND DECREASING FUNCTIONS
On page 33 of your textbook, you see an informal description of increasing and decreasing function. You want to be able to describe these concepts in your own words. The following is a formal description of these same concepts:
1. A function is increasing on an interval I if f(x1) < f(x2) whenever x1 < x2 in the interval I.
2. A function is decreasing on an interval I if f(x1) > f(x2) whenever x1 < x2 in the interval I.
Look over Figure 1.36, 1.37, and 1.38 on pages 29 and 30, observing the domains, ranges, and the increasing or decreasing behavior of special functions that we will use in calculus.
EVEN AND ODD FUNCTIONS
Make sure that your learn the definition of even and odd functions found highlighted on page 15 of your textbook. Also, insure you know which kind of symmetry is associated with each. Do Example 4 at the bottom of page 15 on your own paper so that you can do the same tests of odd or even functions. I warn you to be very careful with the use of parentheses when performing these tests.
COMPOSITE FUNCTIONS
Composite functions are described in the middle of pages 39 through 41of your textbook. You will need to study the material and the examples very carefully so that you understand the concept. With your own paper, work Examples 2 and 3 on page 41 without looking at the solution on that page.
You can now go to the Session 2 assignments to continue your assignment.