The graph illustrates cubic functions
The function of the graph is [tex]\mathbf{ y=(x+2)^3-1}[/tex]
The parent function of a cubic function is:
[tex]\mathbf{y = x^3}[/tex]
From the graph, we can see that [tex]\mathbf{y = x^3}[/tex] is translated 2 units left.
The rule of this translation is:
[tex]\mathbf{(x,y) \to (x + 2,y)}[/tex]
So, the new function becomes
[tex]\mathbf{y = (x + 2)^3}[/tex]
Also, the graph is translated 1 unit down.
The rule of this translation is:
[tex]\mathbf{(x,y) \to (x,y - 1)}[/tex]
So, the new function becomes
[tex]\mathbf{y = (x + 2)^3 - 1}[/tex]
Hence, the equation of the function is:
[tex]\mathbf{y = (x + 2)^3 - 1}[/tex]
Read more about graphs and functions at:
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