Question

drag and drop given $y = \frac{1}{4}x - 6$, find the range when the domain is $\\{-8, -4, 0, 4, 8\\}$. fill in the blanks with the corresponding range value for each domain value to create a table that represents the relation. \

$$\begin{tabular}{|c|c|} \\hline $x$ & $y$ \\\\ \\hline $-8$ & \\\\ \\hline $-4$ & \\\\ \\hline $0$ & \\\\ \\hline $4$ & \\\\ \\hline $8$ & \\\\ \\hline \\end{tabular}$$

$-8$ $-4$ $-7$ $-6$ $-5$

Explanation:

Step1: Substitute \( x = -8 \) into \( y=\frac{1}{4}x - 6 \)

\( y=\frac{1}{4}\times(-8)-6=-2 - 6=-8 \)

Step2: Substitute \( x = -4 \) into \( y=\frac{1}{4}x - 6 \)

\( y=\frac{1}{4}\times(-4)-6=-1 - 6=-7 \)

Step3: Substitute \( x = 0 \) into \( y=\frac{1}{4}x - 6 \)

\( y=\frac{1}{4}\times0 - 6=0 - 6=-6 \)

Step4: Substitute \( x = 4 \) into \( y=\frac{1}{4}x - 6 \)

\( y=\frac{1}{4}\times4 - 6=1 - 6=-5 \)

Step5: Substitute \( x = 8 \) into \( y=\frac{1}{4}x - 6 \)

\( y=\frac{1}{4}\times8 - 6=2 - 6=-4 \)

Table:

\( x \)	\( y \)
\( -4 \)	\( -7 \)
\( 0 \)	\( -6 \)
\( 4 \)	\( -5 \)
\( 8 \)	\( -4 \)

Answer:

For \( x=-8 \), \( y = -8 \); for \( x=-4 \), \( y = -7 \); for \( x = 0 \), \( y=-6 \); for \( x = 4 \), \( y=-5 \); for \( x = 8 \), \( y=-4 \). The filled table is as above.