Question

tabular representations for the functions p, q, and r are given below. write q(x) and r(x) as transformations of p(x).

x	-2	-1	0	1	2

x	-2	-1	0	1	2

x	-2	-1	0	1	2

Explanation:

Step1: Analyze q(x) vs p(x)

Compare corresponding values:
For each $x$, $q(x) = \frac{1}{4}p(x) + 2$
Check: $x=-1$: $\frac{1}{4}(1)+2=2.5$, $x=0$: $\frac{1}{4}(0)+2=2$, matches.

Step2: Analyze r(x) vs p(x)

Compare corresponding values:
For each $x$, $r(x) = 2p(x) - 1$
Check: $x=-2$: $2(4)-1=7$, $x=0$: $2(0)-1=-1$, matches.

Answer:

$q(x) = \frac{1}{4}p(x) + 2$
$r(x) = 2p(x) - 1$