Relations and Function

If your assigned number is

Solve the following Problems

42

3

on pages 708 – 711

3 on pages 719–723

There are many ways to go about solving math problems. To solve this problem, you will be required to do some work that will not be included in the discussion point.

· First, graph your functions so that you can clearly describe the graphs in your post. Your graph itself is not required in your post, although a discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.

· Mention any key points on the graphs, including intercepts, vertex, or start/end points. Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.

· Discuss the general shape and location of each of your graphs.

· State the domain and range for each of your equations. Write them in interval notation.

· State whether each of the equations is a function or not giving your reasons for the answer.

· Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.

· Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing. Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.

· Function

· Relation

· Vertical Line test

· Transformation

Your initial post should be at least 250 words in length.

Question number 3 from 708-711

3

The absolute value function

Graph f(x) = | x |, and state the domain and range.

Solution

To graph this function, we find points that satisfy the equation f(x) = | x|.

Plotting these points, we see that they lie along the V-shaped graph shown in Fig. 11.7. Since any real number can be used for x in f(x) = | x | and since the graph extends without bounds to the left and right, the domain is (−∞, ∞). Because | x | is never negative, the graph does not go below the x-axis. So the range is the set of nonnegative real numbers, [0, ∞).

 

Figure 11.7

Page 703

Now do Exercises 11–12

Helpful Hint

The most important feature of an absolute value function is its V-shape. If we had plotted only points in the first quadrant, we would not have seen the V-shape. So for an absolute value function we always plot enough points to see the V-shape.

Many functions involving absolute value have graphs that are V-shaped, as in Fig. 11.7. To graph functions involving absolute value, we must choose points that determine the correct shape and location of the V-shaped graph.

Question number 3 from 719-723

3 Reflecting

Sketch the graphs of each pair of functions on the same coordinate system. See Example 3.

1.

1. y = x, y = −x

Exercise 19- Reflecting

1.

1.
1.
1.
1.
1.