5.5 Using a Graphing Calculator

Leanne Thompson

5.5 Using a Graphing Calculator

Throughout this unit, we have graphed and analyzed many different relations. This lesson will cover how a graphing calculator can be used to graph and analyze a relation. The instructions outlined in this lesson are for the TI-83 and TI-84 graphing calculators.

Resetting a Calculator

Resetting your calculator will set it back to factory settings.

Table 5.5.1
To reset a calculator:
Press 2nd Press + Select 7: $\downarrow$ Reset Select 1: All RAM… Select 2: Reset

Graphing a Relation

A relation can be graphed in a calculator by inputting the equation of the relation.

Table 5.5.2
To graph a relation:
Press Y= Type the equation of your graph in Y₁. Use the X,T, $\theta$ ,n key to represent your independent variable. Press GRAPH

Practice 1

Graph $y=0.9x+12$ . Draw a rough sketch below.
Note: You will use this relation for Practice 1 through Practice 8.

Blank coordinate plane with x window from -10 to 10 and y window from -10 to 10.

Setting a Window

Notice in Practice 1 that important parts of the graph are cut off. To see more of the graph, the window settings will need to be changed. When you graph relations on your calculator, you often need to change the default window so that you can properly see your graph. The tables below outline what each portion of the window list represents, what the default window in your calculator is, and how to change the window in your calculator.

Table 5.5.3
To set a window:
Press WINDOW. Change number values to change the window and/or scale of your graph.

Table 5.5.4
Definitions	The Default Window
X_minis the minimum x value that will display when graphing an equation. X_maxis the maximum x value that will display when graphing an equation. X_sclis the distance between tick marks on the x-axis. Y_minis the minimum y value that will display when graphing an equation. Y_maxis the maximum y value that will display when graphing an equation. Y_scl is the distance between tick marks on the y-axis. $\downarrow$ X_resis the resolution of the graph. Leave this set as 1.	X_min= –10 X_max= 10 X_scl= 1 Y_min= –10 Y_max= 10 Y_scl= 1 $\downarrow$ X_res= 1

Table 5.5.5
To set a window back to default settings:
Press ZOOM Select 6: ZStandard

When graphing a relation, choose values for your window that will allow you to see important parts of the graph, like the x-intercept and the y-intercept. It is also a good idea to change the window in a way that removes empty space on the graph, as this will allow you to see a more zoomed in version of the graph. To write out a graphing calculator window, you can use the notation x: [x_min, x_max, x_scl] and y: [y_min, y_max,y_scl]. In this notation, the default window would be written as, x: [–10, 10, 1] and y: [–10, 10 ,1].

Practice 2

Make necessary changes to the window so that you can see the x-intercept and the y-intercept on the graph. Write down a suitable window in the notation shown above.

Displaying a Table of Values

After inputting a relation into your calculator, you can display the corresponding table of values on your calculator.

Table 5.5.6
To display a table of values:
Press 2nd Press GRAPH Scroll up and down with the arrow keys to see the different values on the table.

Sometimes the value you want to see on the table of values is difficult to get to by scrolling. If this is the case, you can use the Table Setup (TBLSET) feature on your calculator as outlined.

Table 5.5.7
To find a specific value on the table of values:
Press 2nd Press WINDOW Scroll down and to the right so that your cursor is over top of Ask beside Indpnt Press ENTER Press 2nd Press GRAPH Type the number you would like to see Press ENTER

Practice 3

Display the table of values on your calculator, then fill in the table of values below.

x	y
–10
–5
0
5

Practice 4

Use the Table Setup feature to find the value of y if x = 520.

Finding the y-value of a Point

When given an x value, the corresponding y value of a point can be found using the Value feature. When using the Value feature, make sure that the x value that you are inputting is within the window frame.

Table 5.5.8
To find a y value when given an x value:
Press 2nd Press TRACE Select 1: value Type the value of x Press ENTER The y value will be displayed at the bottom of the graph.

Practice 5

Find the point on the graph where x = –2.

Finding the x-value of a Point

When given a y value, the corresponding x value of a point can be found using the Intersect feature. To find the x value, a second equation will need to be graphed.

Table 5.5.9
To find an x value when given a y value:
Press Y= Graph the equation y = the given y value into Y₂ Press GRAPH Press 2nd Press TRACE Select 5: intersect Use the left or right arrow key to move the cursor close to the intersection point of your two lines. Press ENTER Use the left or right arrow key to move the cursor close to the intersection point of your two lines. Press ENTER Press ENTER The x value will be displayed at the bottom of the graph.

Practice 6

Find the point on the graph where y = 3.

Finding a y-intercept

The y-intercept of a graph can be found by using the Value feature.

Table 5.5.10
To find a y-intercept:
Press 2nd Press TRACE Select 1: value Type 0 to set x = 0 Press ENTER The y-intercept will be displayed at the bottom of the graph.

Practice 7

Find the y-intercept of the graph.

Finding an x-intercept

The x-intercept of a graph can be found by using the zero feature.

Table 5.5.11
To find an x-intercept:
Press 2nd Press TRACE Select 2: zero Use the left or right arrow key to move the cursor directly to the left of the x-intercept. Press ENTER Use your left or right arrow key to move the cursor directly to the right of the x-intercept. Press ENTER Press ENTER The x-intercept will be displayed at the bottom of the graph.

Practice 8

Find the x-intercept of the graph. Round to the nearest hundredth.

Practice 9

Use the following equation to work through this problem: $y = -4x+45$

a) Draw a rough sketch of the graph. Choose a suitable window, and write the equation using the proper notation.
b) Display the table of values to find the value of x when y = 5. Use the Table Setup feature to find the value of y if x = 50.

a)

b)

c) Use the Value feature to find the y value when x = –3.
d) Use the Intersect feature to find the x value when y = 21.

c)

d)

e) Find the y-intercept of the graph.
f) Find the x-intercept of the graph.

e)

f)

Homework

For each of the following provided equations:

Draw a rough sketch.
Write a suitable window.
Identify the x-intercept(s) and the y-intercept.
Identify the missing y value corresponding to the given x value.
Identify the missing x value corresponding to the given y value.

Round to the nearest hundredth where necessary.

a) $y=-3x-20$

Blank coordinate plane

x = –5, y =

y = –10, x =

b) $y=1.5x+12$

Blank coordinate plane

x = –12, y =

y = 10.5, x =

c) $y=4x-60$

Blank coordinate plane

x = 18, y =

y = –56, x =

d) $y=20$

Blank coordinate plane

x = 5, y =

y = 3, x =

e) $y=x^2$

Blank coordinate plane

x = 4, y =

y = 9, x =

f) $y=\frac{3}{4}x-32$

Blank coordinate plane

x = –8, y =

y = –51.29, x =

g) $y=x^2-25$

Blank coordinate plane

x = 0, y =

y = –20, x =

h) $y=2x-\frac{7}{2}$

Blank coordinate plane

x = 3, y =

y = 0.5, x =

i) $y=6x+244$

Blank coordinate plane

x = –30, y =

y = 1 144, x =

Use the following equation to work through this problem: $y = -8x+9$

a) Draw a rough sketch of the graph. Choose a suitable window, and write it using the proper notation.
b) Use the table of values to find the value of y when x = 0.2.

a)

b)

c) Use the Value feature to find the y value when x = –1.5.
d) Use the Intersect feature to find the x value when y = –7.

c)

d)

e) Find the y-intercept of the graph.
f) Find the x-intercept of the graph.

e)

f)

3. Use the following equation to work through this problem: $y = 0.25x-10$

a) Draw a rough sketch of the graph. Choose a suitable window, and write it using the proper notation.
b) Display the table of values to find the value of y when x = 32.

a)

b)

c) Use the Value feature to find the y value when x = –7.
d) Use the Intersect feature to find the x value when y = –9.75.

c)

d)

e) Find the y-intercept of the graph.
f) Find the x-intercept of the graph.

e)

f)

Answers

1.

a)

x: [–10, 5, 1], y: [–30, 10, 5]
x-intercept = –6.67
y-intercept = –20
When x = –5, y = –5.
When y = –10, x = –3.33.

b)

x: [–14, 6, 2], y: [–10, 20, 5]
x-intercept = –8
y-intercept = 12
When x = –12, y = –6.
When y = 10.5, x = –1.

c)

x : [–4, 24, 4], y: [–80, 20, 10]
x-intercept = 15
y-intercept = –60
When x = 18, y = 12.
When y = –56, x = 1.

d)

x: [–10, 10, 1], y: [–5, 25, 5]
x-intercept = none
y-intercept = 20
When x = 5, y = 20.
There is no point on the graph where y = 3.

e)

x: [–10, 10, 1], y: [–10, 10, 1]
x-intercept = 0
y-intercept = 0
When x = 4, y = 16.
When y = 9, x = 3 and x = –3.

f)

x: [–30, 60, 10], y: [–60, 10, 10]
x-intercept = 42.67
y-intercept = –32
When x = –8, y = –38.
When y = –51.29, x = –25.72.

g)

x: [–10, 10, 1], y: [–40, 20, 10]
x-intercepts = –5 and 5
y-intercept = –25
When x = 0, y = –25.
When y = –20, x = –2.24 and x = 2.24.

h)

x: [–2, 5, 1], y: [–10, 5, 1]
x-intercept = 1.75
y-intercept = –3.5
When x = 3, y = 2.5.
When y = 0.5, x = 2.

i)

x: [–60, 200, 50], y: [–100, 1 500, 50]
x-intercept = –40.67
y-intercept = 244
When x = –30, y = 64.
When y = 1 144, x = 150.

2. a) x: [–5, 5, 1], y: [–10, 25, 5]
b) y = 7.4
c) y = 21
d) x = 2
e) y-intercept = 9
f) x-intercept = 1.13

3. a) x: [10, 60, 10], y: [–30, 10, 10]
b) y = –2
c) y = –11.25
d) x = 1
e) y-intercept = –10
f) x-intercept = 40

Attribution

Unless otherwise indicated, material on this page has been adapted from the following resource:

Mazur, I. (2021). Introductory algebra. BCcampus. https://collection.bccampus.ca/textbooks/intermediate-algebra-bccampus-412/, licensed under CC BY 4.0

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Resetting a Calculator

Graphing a Relation

Practice 1

Setting a Window

Practice 2

Displaying a Table of Values

Practice 3

Practice 4

Finding the y-value of a Point

Practice 5

Finding the x-value of a Point

Practice 6

Finding a y-intercept

Practice 7

Finding an x-intercept

Practice 8

Practice 9

Homework

Answers

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