Which of these best represents the function shown in the table?

Question

x f(x)
0 2
1 8
2 32
3 128
4 512

(1 point)
Responses

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

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

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

D. f(x)=x^5

Answer 1

To find the function that best represents the values in the table, let's first look at the values of \( f(x) \) for the corresponding values of \( x \):

• \( f(0) = 2 \)
• \( f(1) = 8 \)
• \( f(2) = 32 \)
• \( f(3) = 128 \)
• \( f(4) = 512 \)

Examining the pattern in the outputs:

1. For \( x = 0 \), \( f(0) = 2 = 2(4^0) \)
2. For \( x = 1 \), \( f(1) = 8 = 2(4^1) \)
3. For \( x = 2 \), \( f(2) = 32 = 2(4^2) \)
4. For \( x = 3 \), \( f(3) = 128 = 2(4^3) \)
5. For \( x = 4 \), \( f(4) = 512 = 2(4^4) \)

From this pattern, we can see that \( f(x) \) can indeed be represented by the function \( f(x) = 2(4^x) \).

Now, let's analyze the options given:

A. \( f(x) = 2(4^x) \) - This matches our observation. B. \( f(x) = x + 2 \) - This is linear and does not fit the values. C. \( f(x) = 6x + 2 \) - This is also linear and does not fit the values. D. \( f(x) = x^5 \) - This is a polynomial function that does not fit the values either.

The best representation of the function shown in the table is:

A. \( f(x) = 2(4^x) \).