The equation that represents the function is [tex]h(x) = x^{2} +2[/tex].
Let us say the function is of form [tex]h(x) = x^{n} +c[/tex]......(1)
What is a Function?
A function is a rule that establishes a relation between two variables.
Points on this graph are (0, 2), (1, 3), (2, 6), and (3, 11).
So, these points will satisfy the graph,
This means, In (1) we can put the given coordinates.
Let us put (0,2)
i.e. [tex]2 = x^0 + c[/tex]
c =2
So (1) becomes [tex]h(x) = x^{n} +2[/tex].....(2)
To get n let us put (2,6) in (2)
[tex]6 = 2^{n} +2\\2^n = 4\\2^n = 2^2\\n = 2[/tex]
So, (2) becomes [tex]h(x) = x^{2} +2[/tex]
Therefore, the equation that represents the function is [tex]h(x) = x^{2} +2[/tex].
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