Use the functions provided below to answer the following questions. multicolumn(2)(|c|)( a(x) ) & multicolumn(2)(c|)( d(x) ) x & y & x & y -1 & -3 & -1 & 3 0 & 0 & 0 & 0 1 & 3 & 1 & -3 2 & 6 & 2 & -6 9) Describe how a(x) was transformed to create d(x) . 10) Identify the value of k . 11) Write d(x) in terms of a(x) .

## Step 1: Analyze the transformation from \( a(x) \) to \( d(x) \)<br />### We need to determine how the function \( a(x) \) is transformed to become \( d(x) \). By comparing the corresponding \( y \)-values for each \( x \) in both tables, we observe:<br />- For \( x = -1 \), \( a(-1) = -3 \) and \( d(-1) = 3 \).<br />- For \( x = 0 \), \( a(0) = 0 \) and \( d(0) = 0 \).<br />- For \( x = 1 \), \( a(1) = 3 \) and \( d(1) = -3 \).<br />- For \( x = 2 \), \( a(2) = 6 \) and \( d(2) = -6 \).<br /><br />### The pattern shows that \( d(x) \) is the negative of \( a(x) \). Therefore, the transformation applied is a reflection over the x-axis.<br /><br />## Step 2: Identify the value of \( k \)<br />### From the transformation identified, \( d(x) = -a(x) \). Here, \( k \) represents the factor by which \( a(x) \) is multiplied to obtain \( d(x) \). Since \( d(x) = -a(x) \), the value of \( k \) is \(-1\).<br /><br />## Step 3: Write \( d(x) \) in terms of \( a(x) \)<br />### Based on the analysis, the relationship between \( d(x) \) and \( a(x) \) can be expressed as:<br />\[ d(x) = -a(x) \]