The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the formg(x) = (x – h)3 + k.

Answer: First optionStep-by-step explanation: By definition, the horizontal shift depends on the value of h and the vertical shift depends on the value of k. [tex]f(x)=(x-h)^3[/tex] indicates that the function if shifted to the right h units. [tex]f(x)=(x+h)^3[/tex] indicates that the  function if shifted to the left h units. [tex]f(x)=f(x)-k[/tex] indicates that the  function if shifted  down k units. [tex]f(x)=f(x)+k[/tex] indicates that the  function if shifted up k units. Then: If h is positive, the graph will shift to the right. If k is negative, the graph will shift down.  As you can see in the graph, the function is shifted 4 units to the right and 2 units down. Therefore g(x) has the form:  [tex]g(x)=(x-4)^3-2[/tex] Where: [tex]h=4\\k=-2[/tex]