Solved on Dec 11, 2023

Complete the table for $f(j) = j^2 + j$ given values of $j$ .

STEP 1

Assumptions
1. The function given is $f(j) = j^{2} + j$ .
2. We need to find the values of $f(j)$ for $j = -5, -3, -1,$ and $1$ .

STEP 2

First, we will calculate $f(j)$ for $j = -5$ . We substitute $j$ with $-5$ into the function.
$f(-5) = (-5)^{2} + (-5)$

STEP 3

Calculate the square of $-5$ and add $-5$ to it.
$f(-5) = 25 - 5$

STEP 4

Now, perform the subtraction to find the value of $f(-5)$ .
$f(-5) = 20$

STEP 5

Next, we will calculate $f(j)$ for $j = -3$ . We substitute $j$ with $-3$ into the function.
$f(-3) = (-3)^{2} + (-3)$

STEP 6

Calculate the square of $-3$ and add $-3$ to it.
$f(-3) = 9 - 3$

STEP 7

Now, perform the subtraction to find the value of $f(-3)$ .
$f(-3) = 6$

STEP 8

Next, we will calculate $f(j)$ for $j = -1$ . We substitute $j$ with $-1$ into the function.
$f(-1) = (-1)^{2} + (-1)$

STEP 9

Calculate the square of $-1$ and add $-1$ to it.
$f(-1) = 1 - 1$

STEP 10

Now, perform the subtraction to find the value of $f(-1)$ .
$f(-1) = 0$

STEP 11

Finally, we will calculate $f(j)$ for $j = 1$ . We substitute $j$ with $1$ into the function.
$f(1) = (1)^{2} + (1)$

STEP 12

Calculate the square of $1$ and add $1$ to it.
$f(1) = 1 + 1$

STEP 13

Now, perform the addition to find the value of $f(1)$ .
$f(1) = 2$

STEP 14

We have now found all the values of $f(j)$ for the given $j$ values. We can complete the table as follows:
\begin{tabular}{|c|c|} \hline $j$ & $f(j)=j^{2}+j$ \\ \hline -5 & 20 \\ \hline -3 & 6 \\ \hline -1 & 0 \\ \hline 1 & 2 \\ \hline \end{tabular}

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Complete the table for $f(j) = j^2 + j$ given values of $j$ .

STEP 1

Assumptions
1. The function given is $f(j) = j^{2} + j$ .
2. We need to find the values of $f(j)$ for $j = -5, -3, -1,$ and $1$ .

STEP 2

First, we will calculate $f(j)$ for $j = -5$ . We substitute $j$ with $-5$ into the function.
$f(-5) = (-5)^{2} + (-5)$

STEP 3

Calculate the square of $-5$ and add $-5$ to it.
$f(-5) = 25 - 5$

STEP 4

Now, perform the subtraction to find the value of $f(-5)$ .
$f(-5) = 20$

STEP 5

Next, we will calculate $f(j)$ for $j = -3$ . We substitute $j$ with $-3$ into the function.
$f(-3) = (-3)^{2} + (-3)$

STEP 6

Calculate the square of $-3$ and add $-3$ to it.
$f(-3) = 9 - 3$

STEP 7

Now, perform the subtraction to find the value of $f(-3)$ .
$f(-3) = 6$

STEP 8

Next, we will calculate $f(j)$ for $j = -1$ . We substitute $j$ with $-1$ into the function.
$f(-1) = (-1)^{2} + (-1)$

STEP 9

Calculate the square of $-1$ and add $-1$ to it.
$f(-1) = 1 - 1$

STEP 10

Now, perform the subtraction to find the value of $f(-1)$ .
$f(-1) = 0$

STEP 11

Finally, we will calculate $f(j)$ for $j = 1$ . We substitute $j$ with $1$ into the function.
$f(1) = (1)^{2} + (1)$

STEP 12

Calculate the square of $1$ and add $1$ to it.
$f(1) = 1 + 1$

STEP 13

Now, perform the addition to find the value of $f(1)$ .
$f(1) = 2$

STEP 14

We have now found all the values of $f(j)$ for the given $j$ values. We can complete the table as follows:
\begin{tabular}{|c|c|} \hline $j$ & $f(j)=j^{2}+j$ \\ \hline -5 & 20 \\ \hline -3 & 6 \\ \hline -1 & 0 \\ \hline 1 & 2 \\ \hline \end{tabular}

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Complete the table for f(j)=j2+jf(j) = j^2 + jf(j)=j2+j given values of jjj.

STEP 1

Assumptions1. The function given is f(j)=j2+j f(j) = j^{2} + j f(j)=j2+j.2. We need to find the values of f(j) f(j) f(j) for j=−5,−3,−1, j = -5, -3, -1, j=−5,−3,−1, and 1 1 1.

STEP 2

First, we will calculate f(j) f(j) f(j) for j=−5 j = -5 j=−5. We substitute j j j with −5-5−5 into the function.f(−5)=(−5)2+(−5)f(-5) = (-5)^{2} + (-5)f(−5)=(−5)2+(−5)

STEP 3

Calculate the square of −5-5−5 and add −5-5−5 to it.f(−5)=25−5f(-5) = 25 - 5f(−5)=25−5

STEP 4

Now, perform the subtraction to find the value of f(−5) f(-5) f(−5).f(−5)=20f(-5) = 20f(−5)=20

STEP 5

Next, we will calculate f(j) f(j) f(j) for j=−3 j = -3 j=−3. We substitute j j j with −3-3−3 into the function.f(−3)=(−3)2+(−3)f(-3) = (-3)^{2} + (-3)f(−3)=(−3)2+(−3)

STEP 6

Calculate the square of −3-3−3 and add −3-3−3 to it.f(−3)=9−3f(-3) = 9 - 3f(−3)=9−3

STEP 7

Now, perform the subtraction to find the value of f(−3) f(-3) f(−3).f(−3)=6f(-3) = 6f(−3)=6

STEP 8

Next, we will calculate f(j) f(j) f(j) for j=−1 j = -1 j=−1. We substitute j j j with −1-1−1 into the function.f(−1)=(−1)2+(−1)f(-1) = (-1)^{2} + (-1)f(−1)=(−1)2+(−1)

STEP 9

Calculate the square of −1-1−1 and add −1-1−1 to it.f(−1)=1−1f(-1) = 1 - 1f(−1)=1−1

STEP 10

Now, perform the subtraction to find the value of f(−1) f(-1) f(−1).f(−1)=0f(-1) = 0f(−1)=0

STEP 11

Finally, we will calculate f(j) f(j) f(j) for j=1 j = 1 j=1. We substitute j j j with 111 into the function.f(1)=(1)2+(1)f(1) = (1)^{2} + (1)f(1)=(1)2+(1)

STEP 12

Calculate the square of 111 and add 111 to it.f(1)=1+1f(1) = 1 + 1f(1)=1+1

STEP 13

Now, perform the addition to find the value of f(1) f(1) f(1).f(1)=2f(1) = 2f(1)=2

STEP 14

We have now found all the values of f(j) f(j) f(j) for the given j j j values. We can complete the table as follows:\begin{tabular}{|c|c|} \hline jjj & f(j)=j2+jf(j)=j^{2}+jf(j)=j2+j \\ \hline -5 & 20 \\ \hline -3 & 6 \\ \hline -1 & 0 \\ \hline 1 & 2 \\ \hline \end{tabular}

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Complete the table for $f(j) = j^2 + j$ given values of $j$ .

Assumptions
1. The function given is $f(j) = j^{2} + j$ .
2. We need to find the values of $f(j)$ for $j = -5, -3, -1,$ and $1$ .

First, we will calculate $f(j)$ for $j = -5$ . We substitute $j$ with $-5$ into the function.
$f(-5) = (-5)^{2} + (-5)$

Calculate the square of $-5$ and add $-5$ to it.
$f(-5) = 25 - 5$

Now, perform the subtraction to find the value of $f(-5)$ .
$f(-5) = 20$

Next, we will calculate $f(j)$ for $j = -3$ . We substitute $j$ with $-3$ into the function.
$f(-3) = (-3)^{2} + (-3)$

Calculate the square of $-3$ and add $-3$ to it.
$f(-3) = 9 - 3$

Now, perform the subtraction to find the value of $f(-3)$ .
$f(-3) = 6$

Next, we will calculate $f(j)$ for $j = -1$ . We substitute $j$ with $-1$ into the function.
$f(-1) = (-1)^{2} + (-1)$

Calculate the square of $-1$ and add $-1$ to it.
$f(-1) = 1 - 1$

Now, perform the subtraction to find the value of $f(-1)$ .
$f(-1) = 0$

Finally, we will calculate $f(j)$ for $j = 1$ . We substitute $j$ with $1$ into the function.
$f(1) = (1)^{2} + (1)$

Calculate the square of $1$ and add $1$ to it.
$f(1) = 1 + 1$

Now, perform the addition to find the value of $f(1)$ .
$f(1) = 2$

We have now found all the values of $f(j)$ for the given $j$ values. We can complete the table as follows:
\begin{tabular}{|c|c|} \hline $j$ & $f(j)=j^{2}+j$ \\ \hline -5 & 20 \\ \hline -3 & 6 \\ \hline -1 & 0 \\ \hline 1 & 2 \\ \hline \end{tabular}