Question

question
select the correct answer.
the function f(x) is given by the table of values.

x	f(x)
2	8
3	27
4	64

if f(x) is shifted 4 units up to obtain g(x), which table of values represents the function g(x)?
four tables of values for g(x) are shown, but their details are partially visible from the image: the first has x values 5,6,7,8? or maybe 1,2,3,4 with g(x) values shifted up by 4?

Explanation:

Step1: Understand Vertical Shift

A vertical shift up by 4 units means we add 4 to each \( f(x) \) value to get \( g(x) \), i.e., \( g(x)=f(x) + 4 \).

Step2: Calculate \( g(x) \) for each \( x \)

• For \( x = 1 \): \( f(1)=1 \), so \( g(1)=1 + 4=5 \)
• For \( x = 2 \): \( f(2)=8 \), so \( g(2)=8 + 4=12 \)
• For \( x = 3 \): \( f(3)=27 \), so \( g(3)=27 + 4=31 \)
• For \( x = 4 \): \( f(4)=64 \), so \( g(4)=64 + 4=68 \)

We check the tables: the table with \( x = 1,2,3,4 \) and \( g(x)=5,12,31,68 \) is the correct one (assuming the second table in the options matches these values, as per calculation).

Answer:

The table (identify by its position or label, e.g., if the second table has \( x = 1,2,3,4 \) and \( g(x)=5,12,31,68 \)) is the correct one. (Assuming the second option in the given choices matches this calculation, so the answer would be the second table option, e.g., if options are labeled A, B, C, D, and B has these values, then B. [Table with x=1,2,3,4 and g(x)=5,12,31,68])