# Modeling, Functions, and Graphs

## SectionB.2Entering Expressions

### SubsectionParentheses

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

#### ExampleB.6.

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

#### ExampleB.7.

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

#### ExampleB.8.

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

#### ExampleB.9.

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

### SubsectionExponents and Powers

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

#### ExampleB.10.

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

#### ExampleB.11.

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

#### ExampleB.12.

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

### SubsectionRoots

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.

#### ExampleB.13.

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

#### ExampleB.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.

#### ExampleB.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).

#### ExampleB.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.

#### ExampleB.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.

### SubsectionAbsolute 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 ).

#### ExampleB.20.

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

### SubsectionScientific Notation

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

#### ExampleB.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 ,.

#### ExampleB.22.

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

#### Troubleshooting.

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.