figure 1.1a evaluating expressions to evaluate an algebraic expression, we may substitute the values...
TRANSCRIPT
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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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
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
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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Separate the commands.
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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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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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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
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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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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
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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)
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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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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Y1 = 2x + 3
(-10, 10, -10, 10)
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)
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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(-4.7, 4.7, -3.1, 3.1)
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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Set the window to the desired setting, and graph the relation.
(-5, 10, -5, 10)
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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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)
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)
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
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
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Y1 = x3 + 2x2 - 4x + 4
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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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)