Question

The graph of g(x) is a translation of y = ³√√x.5329(x)1-10-8-6-4-216 8 10 x4Which equation represents g(x)?Og(x)=√x-4O g(x)=3√√x+4O g(x)=√x+1.5O g(x)=√x-1.5

Answer 1

Consider the function,

`\begin{gathered} f(x)=\sqrt[3]{x} \\ \Rightarrow f(0)=0 \end{gathered}`

Thus, the graph of f(x) crosses (0,0) which is the 'shared' point by the left and right sections of the graph.

In the case of g(x), (0,0) is translated to (4,0).

In general, a horizontal translation is given by the transformation below

`\begin{gathered} h(x)\rightarrow h(x-a)\rightarrow\text{ horizontal shift by a units} \\ a>0\rightarrow\text{ to the right} \\ a<0\rightarrow\text{ to the left} \end{gathered}`

Therefore, in our case,

`\begin{gathered} g(x)=f(x-4)=\sqrt[3]{x-4} \\ \Rightarrow g(x)=\sqrt[3]{x-4} \end{gathered}`

The answer is the first option.