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Modeling, Functions, and Graphs

Section B.2 Entering Expressions

Subsection Parentheses

Order of Operations: The calculator follows the standard order of operations.

Example B.6.

Compute \(2+3\cdot 4\text{.}\) Press
\(2\) + \(3\) × \(4\) ENTER
Ans. \(14\)

Example B.7.

Compute \((2+3)\cdot4\text{.}\) Press
( \(2\) + \(3\) ) × \(4\) ENTER
Ans. \(20\)

Example B.8.

Compute \(\dfrac{1}{2\cdot 3} \text{.}\) Press
\(1 \) ÷ ( \(2\) × \(3\) ) ENTER
Ans. \(0.1666666667\)

Example B.9.

Compute \(\dfrac{1+3}{2} \text{.}\) Press
( \(1 \) + \(3\) ) ÷ \(2\) ENTER
Ans. \(2\)

Subsection Exponents and Powers

Exponents: We use the caret key, ^, to enter exponents or powers.

Example B.10.

Evaluate \(2^{10}\text{.}\)
\(2\) ^ \(10\) ENTER
Ans. \(1024\)
Squaring: There is a short-cut key for squaring, x^2.

Example B.11.

Evaluate \(57^{2}\text{.}\)
\(57\) x^2 ENTER
Ans. \(3249\)
Fractional Exponents: Fractional exponents must be enclosed in parentheses!

Example B.12.

Evaluate \(8^{2/3}\text{.}\)
\(8\) ^ ( \(2\) ÷ \(3 \) ) ENTER
Ans. \(4\)

Subsection Roots

Square Roots: We access the square root by pressing 2nd x^2, and the display shows \(\sqrt{}(\text{.}\) The calculator automatically gives an open parenthesis for the square root, but not a close parenthesis.

Example B.13.

Evaluate \(\sqrt{2} \text{.}\)
2nd x^2 \(2\) ) ENTER
Ans. \(1.414213562\)

Example B.14.

Evaluate \(\sqrt{9+16} \text{.}\)
2nd x^2 \(9\) + \(16\) ) ENTER
Ans. \(5\)
In the next example, note that we must enter ) at the end of the radicand to tell the calculator where the radical ends.

Example B.15.

Evaluate \(\sqrt{9}+16 \text{.}\)
2nd x^2 \(9\) ) + \(16\) ENTER
Ans. \(19\)
Cube Roots: For cube roots, we press MATH to open the Math menu and press \(4\) (see Figure B.16).
two GC settings
Figure B.16.

Example B.17.

Compute \(\sqrt[3]{1728} \text{.}\)
MATH \(~4~\) \(\, 1728\,\) ) ENTER
Ans. \(12\)
For evaluating cube roots and square roots, ) can be omitted if there are no operations following the radical.
Other Roots: For \(n\)th roots, we press MATH to open the Math menu and press \(5\) (see Figure B.16a). The calculator symbol for \(n\)th roots, \(\sqrt[x]{~} \text{,}\) does not include an open parenthesis,(. If the radicand includes an operation, we must enclose it in parentheses.

Example B.18.

Compute \(\sqrt[10]{2\cdot 512} \text{.}\)
\(10\,\)MATH \(~5~\) ( \(2\) × \(512\) ) ENTER
Ans. \(2\)
Notice that we enter the index 10 before the radical symbol.

Subsection Absolute Value

TI calculators use \(abs (x)\) instead of \(\abs{x}\) to denote the absolute value of \(x\text{.}\) The absolute value function is the first entry in the MATH NUM menu (see Figure B.19). The calculator gives ( for the absolute value function, but not ).
GC Math NUM menu
Figure B.19.

Example B.20.

Evaluate \(\dfrac{\abs{21\cdot 54 - 81}}{-9} \text{.}\)
MATH ENTER \(21\) × \(54\) - \(81\) ) ÷ (-) \(9\) ENTER
Ans. \(-117\)

Subsection Scientific Notation

The TI calculators display numbers in scientific notation when the numbers use too many digits to display.

Example B.21.

Compute \(123,456,789^2 \text{.}\) Enter
\(123456789 \) x^2 ENTER
Ans. \(1.524157875 \text{ E }16\)
This is how the calculator displays the number \(1.524157875 \times 10^{16}\text{.}\) Notice that the power \(10^{16}\) is displayed as \(\text{ E }16\text{.}\)
To enter a number in scientific form, we use the key labeled EE, or 2nd ,.

Example B.22.

To enter \(3.26 \times 10^{18}\text{,}\) use the keying sequence
\(3.26\) 2nd , (-) \(18\) ENTER
Ans. \(3.26 \text{ E}\) \(-18\)


GC syntax error screen
Figure B.23.
If your calculator gives you an error message like this, you may have made one of the following common mistakes:
  1. Using the negative key, (-), when you wanted the subtraction key, -, or vice versa.
  2. Omitting a ( or ). Each ( should have a matching ).
Press \(2\) to Go to the error, and see Editing Expressions B.3 below.