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