Determine the rule of the mapping: x -> y where x = [3, 4, 5, 6, 7] and y = [8, 16, 32, 64, 128]

We are given the following pairs of $(x, y)$ values:

• When $x=3$, $y=8$
• When $x=4$, $y=16$
• When $x=5$, $y=32$
• When $x=6$, $y=64$
• When $x=7$, $y=128$

Observe the $y$ values: $8, 16, 32, 64, 128$. These are all powers of 2.

• $8 = 2^3$
• $16 = 2^4$
• $32 = 2^5$
• $64 = 2^6$
• $128 = 2^7$

By comparing the $x$ values with the exponents of 2 for the corresponding $y$ values, we can see a direct relationship:

• For $x=3$, $y=2^3$
• For $x=4$, $y=2^4$
• For $x=5$, $y=2^5$
• For $x=6$, $y=2^6$
• For $x=7$, $y=2^7$ The rule of the mapping is $y = 2^x$.