he function f(x) is given by the table of values. x & 1 & 2 & 3 & 4 f(x) & 1 & 8 & 27 & 64 If f(x) is shifted 4 units up to obtain g(x) , which table of values represents the function g(x) ? x & 5 & 6 & 7 & 8 g(x) & 5 & 12 & 31 & 68 x & 1 & 2 & 3 & 4 g(x) & 5 & 12 & 31 & 68 x & 5 & 6 & 7 & 8 g(x) & 1 & 8 & 27 & 64

## Step 1: Understanding the Function Shift<br />### The function \( f(x) \) is given by the values in the table: \( f(1) = 1 \), \( f(2) = 8 \), \( f(3) = 27 \), and \( f(4) = 64 \). When a function is shifted vertically, each output value is increased or decreased by a constant amount. In this case, \( f(x) \) is shifted 4 units up to obtain \( g(x) \).<br /><br />## Step 2: Calculating \( g(x) \)<br />### To find \( g(x) \), add 4 to each value of \( f(x) \):<br />- \( g(1) = f(1) + 4 = 1 + 4 = 5 \)<br />- \( g(2) = f(2) + 4 = 8 + 4 = 12 \)<br />- \( g(3) = f(3) + 4 = 27 + 4 = 31 \)<br />- \( g(4) = f(4) + 4 = 64 + 4 = 68 \)<br /><br />## Step 3: Matching with Given Tables<br />### Compare the calculated \( g(x) \) values with the tables provided:<br />- The table with \( x \) values 1, 2, 3, 4 and \( g(x) \) values 5, 12, 31, 68 matches our calculations.