Dawnbridge

TI-Nspire CX II field manual for IB Math

Everyone · 15 of 45

15

Building a table of values

All courses

Store a function, choose the x-values the table runs over, and read the value column; then switch the table to Ask so it evaluates x-values you type.

Goal

Tabulate ​f(x)=x3−4x+1​ for ​x=−3​ to ​x=3​ in steps of ​1, then evaluate ​f(2.5).

1

Open the Scratchpad's Graph view with , or through → B: Graph Scratchpad. The cursor lands on the f1(x)= entry line.

2

Type the rule: , then to drop out of the exponent, then . Press to register it.

3

Press . The screen splits: the graph keeps the left pane and a table of values appears on the right. This one shortcut is the whole gesture, and pressing it again removes the table.

4

Choose which x-values the table uses. Press → Table → Edit Table Settings. Set Table Start to ​−3​ and Table Step to ​1, moving between fields with and leaving Independent and Dependent on Auto. to OK and press .

Scratchpad
RAD
Edit Table Settings
Table Start:
-3
Table Step:
1
Independent:
Auto
Dependent:
Auto
OKCancel
5

The table now counts from ​−3​ in steps of ​1. Scroll it with the arrows and it generates more rows in either direction, so it never runs out.

Scratchpad
RAD
xf₁(x)
-3.-14.
-2.1.
-1.4.
0.1.
1.-2.
2.1.
3.16.
6

Read what the column tells you. f1(x) changes sign three times: between ​x=−3​ and ​x=−2, between ​x=0​ and ​x=1, and between ​x=1​ and ​x=2. A sign change means a root in between, so all three roots of this cubic sit inside the table.

7

Now evaluate at a value of your choosing. Reopen Edit Table Settings, set Independent to Ask, and press ENTER on OK. The table empties, and whatever you type into the x-column is evaluated on ENTER. Type .

Scratchpad
RAD
xf₁(x)
2.56.625
Result

​f(2.5)=6.63​ to 3 s.f., and the Auto table brackets all three roots.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Tabulate ​f(x)=x3−6x+2​ from ​x=−3​ to ​x=3​ in steps of ​1. Between which pairs of consecutive integers does ​f​ change sign? Then find ​f(1.4).

  2. 2

    Tabulate ​f(x)=ex−4x​ from ​x=−3​ to ​x=3​ in steps of ​1. Between which pairs of consecutive integers does ​f​ change sign? Then find ​f(1.7).

  3. 3

    Tabulate ​f(x)=x4−5x2+2​ from ​x=−3​ to ​x=3​ in steps of ​1. Between which pairs of consecutive integers does ​f​ change sign? Then find ​f(2.2).