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The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of g (in red). The function f is defined by =fx−x. Write down the expression for gx.

The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of g (in red). The function f is defined by =fx−x class=

Answer :

Solution

- The function is

[tex]f(x)=-\sqrt[]{x}[/tex]

- The graph of g(x) is shifted 4 units down and 2 units right as shown below:

- The transformation is thus

[tex]\begin{gathered} f(x)\to f(x-2)-4 \\ \text{This operation conducts the transformation on the function }f(x) \\ g(x)=f(x-2)-4 \\ g(x)=-\sqrt[]{(x-2)}-4 \end{gathered}[/tex]

Final Answer

The answer is

[tex]g(x)=-\sqrt[]{(x-2)}-4[/tex]

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