TI-Nspire CX II field manual for IB Math
Building a table of values
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.
Tabulate f(x)=x3−4x+1 for x=−3 to x=3 in steps of 1, then evaluate f(2.5).
Open the Scratchpad's Graph view with , or through → B: Graph Scratchpad. The cursor lands on the f1(x)= entry line.
Type the rule: , then to drop out of the exponent, then . Press to register it.
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.
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 .
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.
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.
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 .
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
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
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
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).