Questions: Graphs and Functions Writing an equation for a function after a vertical and horizontal The graph of (f) is translated a whole number of units horizontal The function (f) is defined by (f(x)=sqrtx). Write down the expression for (g(x)). (g(x)=)

Graphs and Functions Writing an equation for a function after a vertical and horizontal The graph of (f) is translated a whole number of units horizontal The function (f) is defined by (f(x)=sqrtx). Write down the expression for (g(x)). (g(x)=)
Transcript text: Graphs and Functions Writing an equation for a function after a vertical and horizontal The graph of $f$ is translated a whole number of units horizontal The function $f$ is defined by $f(x)=\sqrt{x}$. Write down the expression for $g(x)$. \[ g(x)= \]
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Solution

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Solution Steps

Step 1: Identify the transformation

The graph of g is a horizontally shifted version of the graph of f. Specifically, it has been shifted 2 units to the right and 4 units down.

Step 2: Write the transformation mathematically

A horizontal shift to the right by 2 units changes the x to x-2 inside the square root. A vertical shift downwards by 4 units subtracts 4 from the function's output.

Step 3: Write the equation for g(x)

Combining the transformations, we get g(x) = √(x-2) - 4

Final Answer

g(x) = √(x-2) - 4

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