Answer:
[tex]g(x)=\sqrt[3]{x-1}[/tex]
[tex]h(x)=\sqrt[3]{x}-1[/tex]
Step-by-step explanation:
Graph represents the parent function
[tex]f(x)=\sqrt[3]{x}[/tex]
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex]
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From the the given graph it is clear that graph A shifts 1 unit right to get the graph B. So, a=-1, b=0.
[tex]g(x)=\sqrt[3]{x-1}[/tex]
From the the given graph it is clear that graph A shifts 1 unit down to get the graph C. So, a=0, b=-1.
[tex]h(x)=\sqrt[3]{x}-1[/tex]
Therefore, the required functions are [tex]g(x)=\sqrt[3]{x-1}[/tex] and [tex]h(x)=\sqrt[3]{x}-1[/tex].
