Step-by-step explanation:
the key is x = 0.
also I see in the first table no "run-away" effect of some values, so my first suspicion is : it is linear.
let's test it.
a linear function is a line :
y = ax + b
remember, x = 0 is a key element.
y = a×0 + b
-3 = a×0 + b
-3 = b
so, we know, the line function is
y = ax - 3
now, for the a. let's use the next xy pair (1, 1).
1 = a×1 - 3
4 = a
aha ! our line function is therefore
y = 4x - 3
verify with the next 2 points (2, 5) and (3, 9)
5 = 4×2 - 3 = 5 correct
9 = 4×3 - 3 = 9 correct
linear type and equation confirmed.
the second table :
yes, we see relatively big y values compared to the x values.
and the y values follow the powers of 2
so it seems to to be exponential.
64 = 2⁶
32 = 2⁵
16 = 2⁴
8 = 2³
so, while x increases, the powers of 2 decrease. so, we must build something like y = 2^x, but it must run contrary to the increase in x.
the old trick : c-x.
again, x= 0 is key. when x = 0 we get the biggest y (64). that means that gives us c.
64 = 2^(c-x) = 2^(c-0) = 2^c = 2⁶
=> c = 6
so, we suspect the exponential function
y = 2^(6-x)
let's verify with the other points
(1, 32)
32 = 2^(6-1) = 2^(5) = 32 correct
(2, 16)
16 = 2^(6-2) = 2^(4) = 16 correct
(3, 8)
8 = 2^(6-3) = 2^(3) = 8 correct
so, yes, it is the exponential function
y = 2^(6-x)
