Question

skill sheet: key features + connecting tables to models, and regression idea (model form), p. 3
x\t\t\t y
1\t\t\t 4
4\t\t\t 8
9\t\t\t 12

a ( f(x) = 4sqrt{x} )
b ( f(x) = 3sqrt{x} )
c ( f(x) = 4sqrt{2x} )
d ( f(x) = 4sqrt{x - 1} )

Explanation:

Step1: Test Option A with x=1

Substitute \( x = 1 \) into \( f(x)=4\sqrt{x} \), we get \( f(1)=4\sqrt{1}=4 \), which matches the table.

Step2: Test Option A with x=4

Substitute \( x = 4 \) into \( f(x)=4\sqrt{x} \), we get \( f(4)=4\sqrt{4}=4\times2 = 8 \), which matches the table.

Step3: Test Option A with x=9

Substitute \( x = 9 \) into \( f(x)=4\sqrt{x} \), we get \( f(9)=4\sqrt{9}=4\times3 = 12 \), which matches the table.
(We can also check other options for confirmation, but since Option A works for all given x - values, we can conclude.)

Answer:

A. \( f(x) = 4\sqrt{x} \)