& & & & & & & x & y & x & y & & & & -2 & -5 & -2 & 5 & & & & -1 & -1 & -1 & 9 & & & & 0 & 3 & 0 & 18 & & & & 1 & 7 & 1 & 17 & & & & 2 & 15 & 2 & 21 & & & & 2) Complite the tabie to describe p(x) . (Chocse one answer for each column) & multicolumn(2)(|c|)( Type of Trancformation ) & multicolumn(2)(|c|)( K-value ) & multicolumn(2)(|c|)( Description ) & mathrm(n)(mathrm(x))+mathrm(k) & 0 & 10 & 0 & Vertical Shift & mathrm(f)(mathrm(x)+mathrm(k)) & 0 & -10 & 0 & Horizontal Shift & mathrm(k)(mathrm(k) x) & & & & Transformation & mathrm(n)(mathrm(k) x) & & & &

## Step 1: Analyze the Given Tables### We have two functions \( f(x) \) and \( p(x) \) with their respective values for different . The task is to determine the transformation applied to \( f(x) \) to obtain \( p(x) \).## Step 2: Compare Values of \( f(x) \) and \( p(x) \)### By comparing the values from both tables:- For , \( f(-2) = -5 \) and \( p(-2) = 5 \).- For , \( f(-1) = -1 \) and \( p(-1) = 9 \).- For , \( f(0) = 3 \) and \( p(0) = 13 \).- For , \( f(1) = 7 \) and \( p(1) = 17 \).- For , \( f(2) = 11 \) and \( p(2) = 21 \).### Observing these, we see that \( p(x) = f(x) + 10 \).## Step 3: Identify the Transformation Type### From the second image's table, a transformation of the form \( f(x) + k \) with corresponds to a vertical shift.## Step 4: Choose the Correct Options### Based on the analysis, the transformation type is a vertical shift with a -value of 10.