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QuestionFind the values of yy for y=1xy=\frac{1}{x} when x=−4,−3,−2,−1,0,1,2,3,4x = -4, -3, -2, -1, 0, 1, 2, 3, 4.

Studdy Solution

STEP 1

Assumptions1. The function is given as y=1xy=\frac{1}{x}. . We need to find the corresponding yy values for each given xx value in the table.

STEP 2

We will use the function y=1xy=\frac{1}{x} to find the corresponding yy values for each xx value.

STEP 3

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

STEP 4

Calculate the value of yy when x=−4x = -4.
y=1−4=−0.25y = \frac{1}{-4} = -0.25

STEP 5

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

STEP 6

Calculate the value of yy when x=−3x = -3.
y=1−3=−0.33y = \frac{1}{-3} = -0.33

STEP 7

Continue this process for x=−2x = -2.
y=1−2y = \frac{1}{-2}

STEP 8

Calculate the value of yy when x=−2x = -2.
y=1−2=−0.5y = \frac{1}{-2} = -0.5

STEP 9

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

STEP 10

Calculate the value of yy when x=−x = -.
y=−=−y = \frac{}{-} = -

STEP 11

For x=0x =0, the function y=xy=\frac{}{x} is undefined because we cannot divide by zero. So, the yy value for x=0x =0 is undefined.

STEP 12

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

STEP 13

Calculate the value of yy when x=x =.
y==y = \frac{}{} =

STEP 14

Continue this process for x=2x =2.
y=2y = \frac{}{2}

STEP 15

Calculate the value of yy when x=2x =2.
y=2=0.5y = \frac{}{2} =0.5

STEP 16

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

STEP 17

Calculate the value of yy when x=3x =3.
y=3=0.33y = \frac{}{3} =0.33

STEP 18

Finally, substitute x=4x =4 into the function to find the corresponding yy value.
y=4y = \frac{}{4}

STEP 19

Calculate the value of yy when x=4x =4.
y=14=.25y = \frac{1}{4} =.25The completed table is\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hlinexx & -4 & -3 & - & -1 & &1 & &3 &4 \\ \hlineyy & -.25 & -.33 & -.5 & -1 & undefined &1 &.5 &.33 &.25 \\ \hline\end{tabular}

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