Question

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 form
g(x) = (x – h)3 + k.

Answer 1

Answer: First option

Step-by-step explanation:

By definition, the horizontal shift depends on the value of h and the vertical shift depends on the value of k.

$f(x)=(x-h)^3$ indicates that the function if shifted to the right h units.

$f(x)=(x+h)^3$ indicates that the  function if shifted to the left h units.

$f(x)=f(x)-k$ indicates that the  function if shifted  down k units.

$f(x)=f(x)+k$ 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:

 $g(x)=(x-4)^3-2$

Where:

$h=4\\k=-2$