Function transformation involves changing the form of a function
The equation that represents the function f(x) is [tex]f(x) = \sqrt[3] {x + 6} + 1[/tex]
The parent cube root function is:
[tex]y = \sqrt[3] {x}[/tex]
When the function is translated 6 units left, the equation of the function becomes
[tex]y = \sqrt[3] {x + 6}[/tex]
Next, the function is translated 1 unit up.
So, the equation of the function becomes
[tex]y = \sqrt[3] {x + 6} + 1[/tex]
Express as a function
[tex]f(x) = \sqrt[3] {x + 6} + 1[/tex]
Hence, the equation that represents the function f(x) is [tex]f(x) = \sqrt[3] {x + 6} + 1[/tex]
Read more about function transformation at:
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