figure 1.1a evaluating expressions to evaluate an algebraic expression, we may substitute the values...

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Figure 1.1a Evaluating Expressions 2 Evaluate: 4 for . 1, 3,and 2 . 1, 5,and 2 a b b ac a b c a b c To evaluate an algebraic expression, we may subs for the variables and evaluate the numeric expre sure to enclose the values that are substituted For Figure 1.1a, ) ( ) ) ( ( ) ) ( ) ( ( 5 2 1 4 2 1 4 3 x 2 x 2 - - (-) ENTER ENTER Technology 1.1 1 of 3

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Page 1: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Figure 1.1a

Evaluating Expressions2Evaluate: 4 for

. 1, 3, and 2

. 1, 5, and 2

a

b

b ac

a b c

a b c

To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression. Besure to enclose the values that are substituted in parentheses.

For Figure 1.1a,

)(

))(

()

)

()

((

5 214

2143

x2

x2

-

-

(-) ENTER

ENTER

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Page 2: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Evaluating Expressions2Evaluate: 4

. 1, 3, and 2

. 1, 5, and 2

a

b

b ac

a b c

a b cFigure 1.1b

To evaluate an algebraic expression, we may store the values for the variables and enter the algebraic expression. For ease in reading, we will enter all of these commands as one entry. To do so, we separate each commands with a colon, .Store the three values for a, b, and c, separated by colons.

For Figure 1.1b,

ALPHA :

2

B3A

C

1

ALPHAALPHA

ALPHAALPHAALPHAALPHA

::

: ► ►STO

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STO

STO

Enter the expression.

ALPHA B x2 - 4 ALPHA ALPHAA C ENTER

Page 3: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Evaluating Expressions

In order to enter the second expression without retyping, recall the previous entry and edit it. Press to recall the previous entry. Then edit it using the arrow keys in combination with delete, , and insert, .2nd

ENTRY

DEL

2nd

INS

Move the cursor to the left, using the arrow keys. Place the cursor on top of the 3, and delete 3, . Insert the new value for b, -5,

ENTRY2ndDEL

2nd INS (-) 5 ENTER

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2Evaluate: 4

. 1, 3, and 2

. 1, 5, and 2

a

b

b ac

a b c

a b cFigure 1.1b

Page 4: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Testing Algebraic Equations

Determine whether x = 5 is a solution of the equation 4x - 3 = 3x + 2.

Figure 1.2a

Check the value given by evaluating the expression on the left and the expression on the right. Store the given value for the variable, x = 5.

For Figure 1.2a,

5 ►STO

ALPHA :

Enter the right side and the left side separately.

3

4

+

-

2

3 ENTER

ENTERSince 17 = 17, x = 5 is a solution.

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X,T,,n

X,T,,n

X,T,,n

Separate the commands.

1 of 2

Page 5: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Testing Algebraic Equations

Determine whether x = 5 is a solution of the equation 4x - 3 = 3x + 2.

Figure 1.2bFor Figure 1.2a,

Check the value by using the TEST function of the calculator. Store the given value for the variable, x = 5.

5 ►STOSeparate the two commands. ALPHA :

Enter the equation. The equals sign is under TEST menu option 1.

23134 ENTERTEST2nd +-The calculator returns a 1 to indicate that the equation is true and returns a 0 to indicate that the equation is false. Since the calculator returned a 1, x = 5 is a solution of the equation.

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X,T,,n

X,T,,n

X,T,,n

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Page 6: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Table of Values Using Auto Mode

932,

5 x

24,25,26 .

Set the calculator to automatically generate a table of values for y given that x

Figure 1.3a

Set up the table.

Set a minimum value for the independent variable x. (minimum value 24)Set the size of increments to be added to the independent variable. (increments of 1)Set the calculator to perform the evaluations automatically.

For Figure 1.3a,

2nd TBLSET

ENTER42

1 ENTER

ENTERENTER ▼

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Page 7: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

932,

5 x

24,25,26 .

Set the calculator to automatically generate a table of values for y given that x

Figure 1.3bFor Figure 1.3b,

2nd TABLE

Enter the formula in terms of x for the first y.

59(Y= 2) + 3

For Figure 1.3c,

Figure 1.3c

View the table.You may view additional entries in the table by using the up or down arrow keys.

Technology1.3Table of Values

Using Auto Mode

X,T,,n

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Page 8: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Table of Values Using Ask Mode

2nd TBLSET

ENTER ENTER

For Figure 1.4a,

Set the calculator to generate a table of values, asking for the x-values from the user and automatically performing the calculations, for y given that x 9

32,5

x 24,25,26 .

▼►▼

Set up the table.

Set the table to ask mode for the independent variable x. (Ignore the first two entries).

Figure 1.4a

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Page 9: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Table of Values Using Ask Mode

42

2nd

ENTER

59(Y= 2) + 3

5 6

932,

5 x 24,25,26 .

For Figure 1.4b,Enter the formula in terms of x for the first y.

For Figure 1.4c,

View the table. TABLEEnter the values for x.

22 ENTERENTERFigure 1.4c

Figure 1.4b

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Set the calculator to generate a table of values, asking for the x-values from the user and automatically performing the calculations, for y given that x

X,T,,n

2 of 2

Page 10: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Default Graph Screens

Figure 1.6cFigure 1.6bFigure 1.6a

For Figure 1.6a: For a standard screen, choose the Zstandard screen. Enter on your calculator.For Figure 1.6b: For a decimal screen, choose the Zdecimal screen. Enter on your calculator.For Figure 1.6c: For a centered integer screen, choose the Zstandard screen and then choose the Zinteger screen. Enter on your calculator. (Choosing the Zstandard screen first centers the origin on the screen.)Note: To view the screen settings, enter .

6

ZOOMZOOM

4

WINDOW

ENTER

ZOOM

ZOOM

86

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(-10, 10, -10, 10, 1, 1) (-4.7, 4.7, -4.7, 4.7, 1, 1) (-47, 47 10, -31, 31, 10, 1)

Page 11: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Setting Graph Screens

Set the calculator graph screen to (-20, 20, 10, -100, 100, 10, 1).

Figure 1.7bFigure 1.7a

Enter and your choice for each setting, followed by .

For Figure 1.7a,

WINDOW ENTER

02

00

11

0 101

002

ENTERENTER

ENTER

ENTER

ENTER ENTER (-)(-)

0

View the graph.

For Figure 1.7b,

GRAPH

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Page 12: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Graph A Relation

Graph the relation

2 3. y x

Figure 1.8bFigure 1.8a

Enter the equation into the calculator in the Y = menu.For Figure 1.8a,

32Y= +

For Figure 1.8b,

Set the calculator to the desired screen setting and graph. We will usethe default screen.

ZOOM 6

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X,T,,n

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Y1 = 2x + 3

(-10, 10, -10, 10)

Page 13: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Graph A Relation

Graph the relation

2 3. y x

Figure 1.8c

To view the points on the graph, we trace the graph and use the left and right arrow keys to move along the graph. To see the coordinatesof a point that is not traced, enter the value of the independent variable,and then press . For example, we graphed the point ( 1, 5) in Example 5b.

For Figure 1.8c,

ENTER

ENTERTRACE 1

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(-10, 10, -10, 10)

Page 14: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Y-Intercept

2

Determine the -intercept

of the graph of 1.

y

y x

Figure 1.10aEnter the relation in Y1. For Figure 1.10a,

2 1 y x

Y= 1-x2

Set the window to the default decimal screen, and graph the relation.

ZOOM 4

Trace the graph to determine the y-intercept. Since the decimal screen is centered in the window, the first point traced is the y-intercept.

TRACE

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X,T,,n

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(-4.7, 4.7, -3.1, 3.1)

Page 15: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Y-Intercept

2

Determine the -intercept

of the graph of 1.

y

y x

Figure 1.10bFor Figure 1.10b,

Enter the relation in Y1.

Y= x2 - 1

ENTER

ENTER GRAPH

ENTERWINDOW 5▼015(-) ENTER (-)

01Trace the graph to determine the y-intercept. Since the graph is not centered in the window, the first point traced is not the y-intercept. Ask for the y-coordinate when x = 0.

TRACE ENTER0 The y-intercept is ( 0, -1).

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X,T,,n

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Set the window to the desired setting, and graph the relation.

(-5, 10, -5, 10)

Page 16: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

X-Intercepts

3 2

Determine the -intercepts of the

graph of 4.05 3.15 .

x

y x x x

Figure 1.11aFor Figure 1.11a and Figure 1.11b,

3 2Enter the relation 4.05 3.15 in Y1. y x x x

4 0

51

353Y= ++ x2^ .

.

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X,T,,n

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Figure 1.11b

Set the window to the default decimal screen, and graph the relation.

ZOOM 4Trace the graph to determine the x-intercept - that is, the points on the graph where y = 0.

TRACE 1 of 2

(-4.7, 4.7, -3.1, 3.1) (-4.7, 4.7, -3.1, 3.1)

Page 17: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

X-Intercepts

3 2

Determine the -intercepts of the

graph of 4.05 3.15 .

x

y x x x

Figure 1.11c

One of the x-intercepts cannot be found by tracing the graph. To findthis x-intercept, choose ZERO, option 2, under the CALC menu. Press . Trace the graph to the left side of the intercept,called the left bound, and press . Move the cursor to the right of the intercept, called the right bound. Press . Move the cursor as close to the intercept as possible, and press . The calculator will display the coordinates of the missing x-intercept.The x-intercepts are ( 0, 0), ( -3, 0), and ( -1.05, 0).

For Figure 1.11c,

ENTER

CALCENTER

ENTER

22nd

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(-4.7, 4.7, -3.1, 3.1)

Page 18: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Relative Maxima andRelative Minima

Figure 1.12a

3 2( ) 2 4 4. g x x x x

ENTERENTER

ENTER

CALC 42nd

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For Figure 1.12a,

Determine the relative maximum and relative minimum of the function:

First graph the function in Y1.A low point on the graph, ( -2, 12) can be found by tracing the graph. The calculator will estimate a maximum function value between two given values called the left bound and the right bound. Choose MAXIMUM under the CALC function, option 4, by pressing . Move the cursor to the left of the high point and press . Move the cursor to the right of the high point and press . Move the cursor as close as possible to thehigh point and press .Note that the approximation is not exact.The function has a relative maximum of 1 of 2

Y1 = x3 + 2x2 - 4x + 4

(-4.7, 4.7, -3.1, 3.1)

12 at 2. y x

Page 19: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Relative Maxima andRelative Minima

Figure 1.12b

3 2( ) 2 4 4. g x x x x

First graph the function in Y1.A low point on the graph cannot be found by tracing the graph. The calculator will estimate a minimum function value between two given values called the left bound and the right bound. Choose MIMIMUM under the CALC function, option 3, by pressing . Move the cursor to the left of the low point and press . Move the cursor to the right of the low point and press . Move the cursor as close as possible to the low point and press .ENTERENTER ENTER

CALC 32nd

2.5 at 0.7. y x

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For Figure 1.12b,

Determine the relative maximum and relative minimum of the function:

The function has a relative minimum of

2 of 2

Y1 = x3 + 2x2 - 4x + 4

Page 20: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Intersection of Two Graphs

Determine the point of intersection

of the graphs of 2 and 1. y x y xFigure 1.13a

For Figure 1.13a,

Enter 2 as Y1. Move to Y2. Enter 1 as Y2. y x y x

Y= 2 ENTER + 1▼ or

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X,T,,n X,T,,n

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Page 21: Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression

Intersection of Two Graphs

Determine the point of intersection

of the graphs of 2 and 1. y x y x

Figure 1.13b

To check the point of intersection, use INTERSECT under the CALC menu, option 5,by pressing . Move the cursor to the closest location to the intersection on the first graph, and press . Move the cursor to the closest location to the intersection on the second graph, and press . Move as close as possible to the intersection point, and press .The point of intersection is ( 1, 2).

ENTER52nd

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Trace the graphs to find their intersection by using the left and right arrow keys. To move between the graphs, use the up and down arrow keys. The point of intersection is ( 1, 2).

For Figure 1.13b,

Graph the curve on a decimal screen.ZOOM 4

ENTER

CALC

ENTER

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(-4.7, 4.7, -3.1, 3.1)