TECHNOLOGY EXTENSION Solving Inequalities With a Graphing Calculator

TECHN O LO G Y EX TEN SI O N

Solving Inequa lities W ith a Gra phing Ca lcula tor

Di sp l a y i n g a So l u t i o n

Some graphing calculators can be used to display the solution to an inequality in one variable.

To display the solution to 2x + 1 < 3x - 2, choose

the dot mode from the mode settings, and enter the inequality in the Y= editor as follows. You can enter the inequality symbol using the TEST menu.

Y1 = 2X + 1 < 3X - 2

Then, graph Y1 in the standard viewing window.

1. Using paper and pencil, solve the inequality algebraically and graph the solution.

2. Compare your graph from question 1 with the way the calculator displays the solution.

3. Using the TRACE instruction, find the values of x in the solution.

4. Describe how each of the following can be used to give a more accurate answer than you found in question 3. a) the ZOOM menu

b) the U key and the TABLE SETUP screen

c) changing the window variables

5. a) Using the TRACE instruction, find the value

of y for each value of x in the solution.

b) Explain why the graph of the solution does not lie on the x-axis.

6. Graph Y1 using the connected mode instead of the dot mode. Explain why the dot mode should be used.

7. a) Modify the inequality by changing the < symbol to . Display the solution on the calculator.

b) Does the graphing calculator distinguish between

< and ? Explain.

82 MHR ? Chapter 1

So l v i n g I n e q u a l i t i e s

8. Display the solution to each of

the following inequalities using a

graphing calculator. In your

notebook, sketch each display and

describe how it should be modified

to show the solution fully. State the

solution to each inequality.

a) 2x + 3 7 b) 3x - 1 < 8

c) 2x - 3 > -x d) 5x + 8 4x + 5

e) -4x + 2 -2 f) 3x + 2 5x - 6

g) 2(x - 3) 4x - 2

h) 3(x - 1) - x > 4(x + 1) - 1

i) 23x x - 1

j)

34x

+

23x

-

5

6

<

2(x

-

1)

k)

x-1 2

<

x-2 3

l)

3

+

x-3 6

x

m) x - 2 3x - 1

n) 4(x + 2) > 2(5 - x)

9. Some graphing calculators, such as the T I-92 and T I-92 Plus, have the capability to solve inequalities algebraically. If this type of calculator is available, use the solve function to solve the inequalities in question 8. T he inequality symbols are found in the test submenu.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download