Question

For the rule y= 4 - x2, calculate the y-values that complete the table below

The first value is given for you.
IN (x) -3 -2 -1 0 1 2 3
OUT (y) -5​

Answer 1

`\begin{center}\begin{tabular} c x & y=4-x^2 \\  -3 & -5 \\   -2 & 0\\-1 & 3 \\   0 &4 \\   1&3\\2&0\\3&-5\end{tabular}\end{center}`

Explanation:

The given function is
`y=4-x^2`

When x=-2 we have
`y=4-(-2)^2=4-4=0`

When x=-1 we have
`y=4-(-1)^2=4-1=3`

When x=0 we have
`y=4-(0)^2=4-0=4`

When x=1 we have
`y=4-(1)^2=4-1=3`

When x=2 we have
`y=4-(2)^2=4-4=0`

When x=3 we have
`y=4-(3)^2=4-9=-5`

The complete table is

`\begin{center}\begin{tabular}  c x & y=4-x^2 \\  -3 & -5 \\   -2 & 0\\-1 & 3 \\   0 &4 \\   1&3\\2&0\\3&-5\end{tabular}\end{center}`