Question

Given the parent function g(x)=x√ which function has a graph that has been translated 3 to the left and reflected in the x-axis?g(x)=−x+3−−−−−−√g of x is equal to square root of negative x plus 3 end rootf(x)=−x+3−−−−−√f of x is equal to negative square root of x plus 3 end rootf(x)=−x−3−−−−−√f of x is equal to negative square root of x minus 3 end rootg(x)=−x−3−−−−−−√

Answer 1

Step 1:

Rule for translation of a function to the left.

If a function of f(x) = x is translated to the left by a units, the function becomes f(x) = x + a

Rule for reflection across x-axis

The rule for a reflection over the x -axis is (x,y)→(x,−y)

Step 2:

`\begin{gathered} g(x)\text{ = }\sqrt[]{x} \\ \text{When translated 3 units to the left, the function becomes} \\ g(x)\text{ = }\sqrt[]{x\text{ + 3}} \\ \text{when reflected over x-axis} \\ g(x)\text{ = -}\sqrt[]{\text{x + 3}} \end{gathered}`

Final answer

`f(x)\text{ = -}\sqrt[]{x\text{ + 3}}`