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

Question

Pergunta

Answer 1

###

$\begin{array}{|c|c|c|c|c|}\hline\ x\ \ &\ 1\ &\ 2\ &\ 3\ &\ 4\ \\\hline\ g(x)\ \ &\ 5\ &\ 12\ &\ 31\ &\ 68\ \\\hline\end{array}$

Answer 2

## Step 1: Understanding the Function Shift
### 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

$g(x)$ .

## Step 2: Calculating

$g(x)$
### To find

$g(x)$ , add 4 to each value of

$f(x)$ :
-

$g(1) = f(1) + 4 = 1 + 4 = 5$
-

$g(2) = f(2) + 4 = 8 + 4 = 12$
-

$g(3) = f(3) + 4 = 27 + 4 = 31$
-

$g(4) = f(4) + 4 = 64 + 4 = 68$

## Step 3: Matching with Given Tables
### Compare the calculated

$g(x)$ values with the tables provided:
- The table with

$x$ values 1, 2, 3, 4 and

$g(x)$ values 5, 12, 31, 68 matches our calculations.