Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression. Be sure to enclose the values that are substituted in parentheses. For Figure 1.1a, )( ))( () ) () (( x2x2 x2x2 - - (-) ENTER Technology of 3

Evaluating Expressions Figure 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 :: : ► ► ► Technology of 3 Enter the expression. ALPHA Bx2x2 -4 AC 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, ENTRY 2nd DEL 2nd INS (-)5 ENTER Technology of 3 Figure 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 ► ALPHA : Enter the right side and the left side separately ENTER Since 17 = 17, x = 5 is a solution. Technology 1.2 X,T, ,n Separate the commands. 1 of 2

Testing Algebraic Equations Determine whether x = 5 is a solution of the equation 4x - 3 = 3x + 2. Figure 1.2b For Figure 1.2a, Check the value by using the TEST function of the calculator. Store the given value for the variable, x = 5. 5 ► Separate the two commands. ALPHA : Enter the equation. The equals sign is under TEST menu option ENTERTEST 2nd+- 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. Technology 1.2 X,T, ,n 2 of 2

Table of Values Using Auto Mode 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, 2ndTBLSET ENTER42 1 ▼ Technology of 2

Set the calculator to automatically generate a table of values for y given that x Figure 1.3b For Figure 1.3b, 2ndTABLE Enter the formula in terms of x for the first y. 5  9(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. Technology 1.3 Table of Values Using Auto Mode X,T, ,n 2 of 2

Table of Values Using Ask Mode 2ndTBLSET 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 ▼►▼ Set up the table. Set the table to ask mode for the independent variable x. (Ignore the first two entries). Figure 1.4a Technology of 2

Table of Values Using Ask Mode 42 2nd ENTER 5  9(Y=2)+3 56 For Figure 1.4b, Enter the formula in terms of x for the first y. For Figure 1.4c, View the table. TABLE Enter the values for x. 22ENTER Figure 1.4c Figure 1.4b Technology 1.4 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

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 ZOOM 4 WINDOW ENTER ZOOM 86 Technology 1.6 (-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, WINDOWENTER (-) 0 View the graph. For Figure 1.7b, GRAPH Technology 1.7

Graph A Relation Figure 1.8b Figure 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 use the default screen. ZOOM6 Technology 1.8 X,T, ,n 1 of 2 Y1 = 2x + 3 (-10, 10, -10, 10)

Graph A Relation 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 coordinates of 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 TRACE1 Technology of 2 (-10, 10, -10, 10)

Y-Intercept Figure 1.10a Enter the relation in Y1. For Figure 1.10a, Y=1-x2x2 Set the window to the default decimal screen, and graph the relation. ZOOM4 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 Technology 1.10 X,T, ,n 1 of 2 (-4.7, 4.7, -3.1, 3.1)

Y-Intercept Figure 1.10b For Figure 1.10b, Enter the relation in Y1. Y=x2x2 -1 ENTER GRAPH ENTERWINDOW5▼015(-)ENTER(-) 01 Trace 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. TRACEENTER0 The y-intercept is ( 0, -1). Technology 1.10 X,T, ,n 2 of 2 Set the window to the desired setting, and graph the relation. (-5, 10, -5, 10)

X-Intercepts Figure 1.11a For Figure 1.11a and Figure 1.11b, Y=++x2x2 ^.. Technology 1.11 X,T, ,n Figure 1.11b Set the window to the default decimal screen, and graph the relation. ZOOM4 Trace 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)

X-Intercepts Figure 1.11c One of the x-intercepts cannot be found by tracing the graph. To find this 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 CALC ENTER 22nd Technology of 2 (-4.7, 4.7, -3.1, 3.1)

Relative Maxima and Relative Minima Figure 1.12a ENTER CALC42nd Technology 1.12 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 the high point and press. Note that the approximation is not exact. The function has a relative maximum of 1 of 2 Y1 = x 3 + 2x 2 - 4x + 4 (-4.7, 4.7, -3.1, 3.1)

Relative Maxima and Relative Minima Figure 1.12b 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. ENTER CALC32nd Technology 1.12 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 = x 3 + 2x 2 - 4x + 4

Intersection of Two Graphs Figure 1.13a For Figure 1.13a, Y=2ENTER+1▼ or Technology 1.13 X,T, ,n 1 of 2

Intersection of Two Graphs 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). ENTER 52nd Technology 1.13 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. ZOOM4 ENTER CALC ENTER 2 of 2 (-4.7, 4.7, -3.1, 3.1)