Use the table to answer the question below.

Question

x F(x)
0 2
1 8
2 32
3 128
4 512
Which of these best represents the function shown in the table?

(1 point)
Responses

f(x)=2(4x)
f of x is equal to 2 times open paren 4 to the x th power close paren

f(x)=x+2
f of x is equal to x plus 2

f(x)=6x+2
f of x is equal to 6 x plus 2

f(x)=x5
f of x is equal to x to the 5th power
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Answer 1

To determine which function best represents the values in the table, let's analyze the values given for \( F(x) \):

• For \( x = 0 \), \( F(x) = 2 \)
• For \( x = 1 \), \( F(x) = 8 \)
• For \( x = 2 \), \( F(x) = 32 \)
• For \( x = 3 \), \( F(x) = 128 \)
• For \( x = 4 \), \( F(x) = 512 \)

Noticing the values, we can see that:

• \( F(0) = 2 = 2 \times 4^0 \)
• \( F(1) = 8 = 2 \times 4^1 \)
• \( F(2) = 32 = 2 \times 4^2 \)
• \( F(3) = 128 = 2 \times 4^3 \)
• \( F(4) = 512 = 2 \times 4^4 \)

From this pattern, we can conclude that:

\[ F(x) = 2(4^x) \]

Therefore, the best representation of the function shown in the table is:

f(x) = 2(4^x)