Function transformation involves changing the form of a function.
The equation of the translated function is [tex]f(x) = \sqrt[3]{x + 6} + 1[/tex]
The parent function is given as:
[tex]f(x) = \sqrt[3]{x}[/tex]
First, the function is shifted left by 6 units.
The rule of this translation is:
[tex](x,y) \to (x + 6,y)[/tex]
So, we have:
[tex]f(x) = \sqrt[3]{x + 6}[/tex]
Next, the function is shifted up by 1 unit.
The rule of this translation is:
[tex](x,y) \to (x,y+1)[/tex]
So, we have:
[tex]f(x) = \sqrt[3]{x + 6} + 1[/tex]
Hence, the equation of the translated function is [tex]f(x) = \sqrt[3]{x + 6} + 1[/tex]
Read more about function transformation at:
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