26.7: A.7- Special functions (absolute value, n-th root, etc.)

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Thomas Tradler and Holly Carley
CUNY New York City College of Technology via New York City College of Technology at CUNY Academic Works

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We now point out some important functions in the MATH menu ($\boxed{\text{math}}$) and the LIST menu ($\boxed{\text{2nd}}$$\boxed{\text{stat}}$), that are used in this course.

Fractions

Suppose in the main screen you evaluate $4/6$. Your calculator will display $.66666666667$. If you wanted to see this as a fraction you would type $\boxed{\text{math}}$$\boxed{\text{enter}}$$\boxed{\text{enter}}$. You will now see $2/3$ displayed.

Absolute value

To evaluate $|-4|$ you would type in the main screen $\boxed{\text{math}}$$\boxed{\triangleright}$$\boxed{\text{enter}}$$\boxed{\text{(-)}}$$\boxed{\text{4}}$$\boxed{\text{enter}}$. The answer $4$ should be displayed. To graph $|x-2|$, go to the Y= screen ($\boxed{y=}$) and enter in the Y1 (for example) space $\boxed{\text{math}}$$\boxed{\triangleright}$$\boxed{\text{enter}}$$\boxed{\text{X,T,}\theta,n}$$\boxed{\text{-}}$$\boxed{\text{2}}$$\boxed{\triangleright}$$\boxed{\text{enter}}$.

$clipboard_e9bde1ace956cd3e8402f7cebe8f58604.png$

Now you can go to the graphing screen to see the graph.

$n$-th root

To calculate the cube root of $8$. Press on the main screen $\boxed{\text{3}}$$\boxed{\text{math}}$$\boxed{\text{5}}$ (or select the x-root) $\boxed{\text{8}}$$\boxed{\text{enter}}$.

$clipboard_eba2991b42ed37fde034d5285d203bfd6.png$

You can compute any root this way (e.g. the $5$th root of $7$). For the cube root you can also use $\boxed{\text{math}}$$\boxed{\text{4}}$ instead. Recall also the algebraic definition of the $n$th root,

\[\sqrt[n]{x}=x^{\frac{1}{n}} \nonumber \]

so that the $5$th root of $7$ can also be computed by pressing $\boxed{\text{7}}$$\boxed{\wedge}$$\boxed{\text{(}}$$\boxed{\text{1}}$$\boxed{\div}$$\boxed{\text{5}}$$\boxed{\text{)}}$.

Factorials

To compute $5!$, for example, in the main screen type $\boxed{\text{5}}$$\boxed{\text{math}}$ then move the cursor to the right three times (or left once) so that the ’PRB’ menu is displayed. Option 4 is ’$!$’ so press $\boxed{\text{4}}$ or move the cursor to highlight this option and press $\boxed{\text{enter}}$. Finally press $\boxed{\text{enter}}$ and the answer $120$ will be displayed.

$clipboard_e2e178d1289538f1b0de9557e24addc05.png$

Combinations and permutations

To calculate $_{5} C_{2}=\dbinom{5}{2}$, in the main menu type $\boxed{\text{5}}$. Then go to the math-probability menu by pressing $\boxed{\text{math}}$ then the right (or left) arrow until ’PRB’ is highlighted. You will see that the third option is $_nC_r$ so press $\boxed{\text{3}}$. This will return you to the main screen. Press $\boxed{\text{2}}$$\boxed{\text{enter}}$. The answer $10$ will be displayed.

$clipboard_eb518cfa3d49bb14140f7232bdba2c448.png$

Permutations $_nP_r$ are handled the same way except it is the second option under the math-probability menu instead of the third.

Sequences and series

A sequence $a_1,a_2,a_3,\dots$ that is given by a formula can be added via the ‘LIST’ menu (press $\boxed{\text{2nd}}$$\boxed{\text{stat}}$). For example, to enter the first $10$ terms $a_1,a_2,\dots, a_{10}$ of the sequence $a_n=n^2+1$, we have to write $seq(x^2+1,x,1,10)$. Here, the ‘sequence’ command takes four inputs, first the assignment $x^2+1$, second the independent variable $x$, third the starting index $1$, and fourth the final index $10$. This expression is entered to the calculator by pressing $\boxed{\text{2nd}}$$\boxed{\text{stat}}$$\boxed{\triangleright}$$\boxed{\text{5}}$$\boxed{\text{X,T,}\theta,n}$$\boxed{x^2}$$\boxed{\text{+}}$$\boxed{\text{1}}$$\boxed{\text{,}}$$\boxed{\text{X,T,}\theta,n}$$\boxed{\text{,}}$$\boxed{\text{1}}$$\boxed{\text{,}}$$\boxed{\text{1}}$$\boxed{\text{0}}$$\boxed{\text{)}}$ and then confirmed by pressing $\boxed{\text{enter}}$. We obtain:

$clipboard_e94ce16d279929b2c01e928753648dc23.png$

To add the ten numbers $a_1+\dots +a_{10}$ of the sequence, we use the ‘sum’ command in the LIST-MATH menu. Press $\boxed{\text{2nd}}$$\boxed{\text{stat}}$$\boxed{\triangleleft}$$\boxed{\text{5}}$ to enter the ‘$sum($’ expression. Then using the previously entered answer by pressing $\boxed{\text{2nd}}$$\boxed{\text{(-)}}$, and finishing with $\boxed{\text{)}}$$\boxed{\text{enter}}$, we now calculate the wanted sum.

$clipboard_e45e5e22522f43bdbbadd970b5ef60192.png$

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Fractions

Absolute value

\(n\)-th root

Factorials

Combinations and permutations

Sequences and series