Answer:
[tex]y=x^3+4[/tex]
Step-by-step explanation:
From the equation, we know that we are looking for an equation in the form of [tex]y=x^a+b[/tex].
Due to this, we need to look for the nearest perfect squares or cubes.
Let's look at squares first.
x=1, the two nearest are 1 and 9, both of which are 4 away
x=2, the two nearest are 9 and 16, which are 3 and 4 away
x=3, the two nearest are 25 and 36, which are 6 and 5 away.
It is clear that there is no pattern here, so let us move to perfect cubes
x=1, 1 is 4 less than 5
x=2, 8 is 4 less than 12
x=3, 27 is 4 less than 31
It can be seen that there is a clear pattern here.
We can see that the first part of the equation would be [tex]x^3[/tex], and the second would be [tex]+4[/tex].
This means that our answer would be
[tex]y=x^3+4[/tex]
