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