QuestionFind $y$ for $y=\frac{1}{x}$ when $x$ is -4, -3, -2, -1, 0, 1, 2.

Studdy Solution

STEP 1

Assumptions1. The function given is $y=\frac{1}{x}$ . We need to find the corresponding $y$ values for the given $x$ values in the table

STEP 2

The function $y=\frac{1}{x}$ means that for each $x$ value, the corresponding $y$ value is obtained by taking the reciprocal of $x$ .

STEP 3

Let's start with the first $x$ value in the table, which is -. Substitute $x=-$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-}$

STEP 4

Calculate the value of $y$ .
$y=\frac{1}{-4} = -0.25$

STEP 5

Next, substitute $x=-3$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-3}$

STEP 6

Calculate the value of $y$ .
$y=\frac{1}{-3} = -0.33$

STEP 7

Next, substitute $x=-2$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-2}$

STEP 8

Calculate the value of $y$ .
$y=\frac{1}{-2} = -0.5$

STEP 9

Next, substitute $x=-$ into the function to find the corresponding $y$ value.
$y=\frac{}{-}$

STEP 10

Calculate the value of $y$ .
$y=\frac{}{-} = -$

STEP 11

Next, substitute $x=0$ into the function to find the corresponding $y$ value.
$y=\frac{}{0}$

STEP 12

The value of $y$ is undefined when $x=0$ because division by zero is undefined in mathematics. So, for $x=0$ , $y$ is undefined.

STEP 13

Next, substitute $x=$ into the function to find the corresponding $y$ value.
$y=\frac{}{}$

STEP 14

Calculate the value of $y$ .
$y=\frac{}{} =$

STEP 15

Next, substitute $x=2$ into the function to find the corresponding $y$ value.
$y=\frac{}{2}$

STEP 16

Calculate the value of $y$ .
$y=\frac{}{2} =0.5$ So, the completed table is\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline $x$ & -4 & -3 & -2 & - &0 & &2 \\ \hline $y$ & -0.25 & -0.33 & -0.5 & - & undefined & &0.5 \\ \hline\end{tabular}

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QuestionFind $y$ for $y=\frac{1}{x}$ when $x$ is -4, -3, -2, -1, 0, 1, 2.

Studdy Solution

STEP 1

Assumptions1. The function given is $y=\frac{1}{x}$ . We need to find the corresponding $y$ values for the given $x$ values in the table

STEP 2

The function $y=\frac{1}{x}$ means that for each $x$ value, the corresponding $y$ value is obtained by taking the reciprocal of $x$ .

STEP 3

Let's start with the first $x$ value in the table, which is -. Substitute $x=-$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-}$

STEP 4

Calculate the value of $y$ .
$y=\frac{1}{-4} = -0.25$

STEP 5

Next, substitute $x=-3$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-3}$

STEP 6

Calculate the value of $y$ .
$y=\frac{1}{-3} = -0.33$

STEP 7

Next, substitute $x=-2$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-2}$

STEP 8

Calculate the value of $y$ .
$y=\frac{1}{-2} = -0.5$

STEP 9

Next, substitute $x=-$ into the function to find the corresponding $y$ value.
$y=\frac{}{-}$

STEP 10

Calculate the value of $y$ .
$y=\frac{}{-} = -$

STEP 11

Next, substitute $x=0$ into the function to find the corresponding $y$ value.
$y=\frac{}{0}$

STEP 12

The value of $y$ is undefined when $x=0$ because division by zero is undefined in mathematics. So, for $x=0$ , $y$ is undefined.

STEP 13

Next, substitute $x=$ into the function to find the corresponding $y$ value.
$y=\frac{}{}$

STEP 14

Calculate the value of $y$ .
$y=\frac{}{} =$

STEP 15

Next, substitute $x=2$ into the function to find the corresponding $y$ value.
$y=\frac{}{2}$

STEP 16

Calculate the value of $y$ .
$y=\frac{}{2} =0.5$ So, the completed table is\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline $x$ & -4 & -3 & -2 & - &0 & &2 \\ \hline $y$ & -0.25 & -0.33 & -0.5 & - & undefined & &0.5 \\ \hline\end{tabular}

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QuestionFind yyy for y=1xy=\frac{1}{x}y=x1​ when xxx is -4, -3, -2, -1, 0, 1, 2.

Studdy Solution

STEP 1

Assumptions1. The function given is y=1xy=\frac{1}{x}y=x1​ . We need to find the corresponding yyy values for the given xxx values in the table

STEP 2

The function y=1xy=\frac{1}{x}y=x1​ means that for each xxx value, the corresponding yyy value is obtained by taking the reciprocal of xxx.

STEP 3

Let's start with the first xxx value in the table, which is -. Substitute x=−x=-x=− into the function to find the corresponding yyy value.y=1−y=\frac{1}{-}y=−1​

STEP 4

Calculate the value of yyy.y=1−4=−0.25y=\frac{1}{-4} = -0.25y=−41​=−0.25

STEP 5

Next, substitute x=−3x=-3x=−3 into the function to find the corresponding yyy value.y=1−3y=\frac{1}{-3}y=−31​

STEP 6

Calculate the value of yyy.y=1−3=−0.33y=\frac{1}{-3} = -0.33y=−31​=−0.33

STEP 7

Next, substitute x=−2x=-2x=−2 into the function to find the corresponding yyy value.y=1−2y=\frac{1}{-2}y=−21​

STEP 8

Calculate the value of yyy.y=1−2=−0.5y=\frac{1}{-2} = -0.5y=−21​=−0.5

STEP 9

Next, substitute x=−x=-x=− into the function to find the corresponding yyy value.y=−y=\frac{}{-}y=−​

STEP 10

Calculate the value of yyy.y=−=−y=\frac{}{-} = -y=−​=−

STEP 11

Next, substitute x=0x=0x=0 into the function to find the corresponding yyy value.y=0y=\frac{}{0}y=0​

STEP 12

The value of yyy is undefined when x=0x=0x=0 because division by zero is undefined in mathematics. So, for x=0x=0x=0, yyy is undefined.

STEP 13

Next, substitute x=x=x= into the function to find the corresponding yyy value.y=y=\frac{}{}y=​

STEP 14

Calculate the value of yyy.y==y=\frac{}{} =y=​=

STEP 15

Next, substitute x=2x=2x=2 into the function to find the corresponding yyy value.y=2y=\frac{}{2}y=2​

STEP 16

Calculate the value of yyy.y=2=0.5y=\frac{}{2} =0.5y=2​=0.5So, the completed table is\begin{tabular}{|l|l|l|l|l|l|l|l|} \hlinexxx & -4 & -3 & -2 & - &0 & &2 \\ \hlineyyy & -0.25 & -0.33 & -0.5 & - & undefined & &0.5 \\ \hline\end{tabular}

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QuestionFind $y$ for $y=\frac{1}{x}$ when $x$ is -4, -3, -2, -1, 0, 1, 2.

Assumptions1. The function given is $y=\frac{1}{x}$ . We need to find the corresponding $y$ values for the given $x$ values in the table

The function $y=\frac{1}{x}$ means that for each $x$ value, the corresponding $y$ value is obtained by taking the reciprocal of $x$ .

Let's start with the first $x$ value in the table, which is -. Substitute $x=-$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-}$

Calculate the value of $y$ .
$y=\frac{1}{-4} = -0.25$

Next, substitute $x=-3$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-3}$

Calculate the value of $y$ .
$y=\frac{1}{-3} = -0.33$

Next, substitute $x=-2$ into the function to find the corresponding $y$ value.
$y=\frac{1}{-2}$

Calculate the value of $y$ .
$y=\frac{1}{-2} = -0.5$

Next, substitute $x=-$ into the function to find the corresponding $y$ value.
$y=\frac{}{-}$

Calculate the value of $y$ .
$y=\frac{}{-} = -$

Next, substitute $x=0$ into the function to find the corresponding $y$ value.
$y=\frac{}{0}$

The value of $y$ is undefined when $x=0$ because division by zero is undefined in mathematics. So, for $x=0$ , $y$ is undefined.

Next, substitute $x=$ into the function to find the corresponding $y$ value.
$y=\frac{}{}$

Calculate the value of $y$ .
$y=\frac{}{} =$

Next, substitute $x=2$ into the function to find the corresponding $y$ value.
$y=\frac{}{2}$

Calculate the value of $y$ .
$y=\frac{}{2} =0.5$ So, the completed table is\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline $x$ & -4 & -3 & -2 & - &0 & &2 \\ \hline $y$ & -0.25 & -0.33 & -0.5 & - & undefined & &0.5 \\ \hline\end{tabular}