Write an equation for the function that is described by the given characteristic.
The shape of $f ( x ) = \sqrt { x }$ ,but shifted three units to the left and reflected in both the x-axis and the y-axis.

A) $g ( x ) = \sqrt { - x + 3 }$
B) $g ( x ) = - \sqrt { x + 3 }$
C) $g ( x ) = - \sqrt { - x + 3 }$
D) $g ( x ) = \sqrt { x + 3 }$
E) $g ( x ) = - \sqrt { - x - 3 }$

Question

Write an equation for the function that is described by the given characteristic. ​
The shape of $f ( x ) = \sqrt { x }$ ,but shifted three units to the left and reflected in both the x-axis and the y-axis.
​
A) $g ( x ) = \sqrt { - x + 3 }$
B) $g ( x ) = - \sqrt { x + 3 }$
C) $g ( x ) = - \sqrt { - x + 3 }$
D) $g ( x ) = \sqrt { x + 3 }$
E) $g ( x ) = - \sqrt { - x - 3 }$

Quizplus · Accepted Answer

Shifting $f(x) = \sqrt{x}$ three units to the left involves replacing $x$ with $x + 3$, resulting in $\sqrt{x + 3}$. Reflecting this in the y-axis changes $x$ to $-x$, giving $\sqrt{-x + 3}$. Reflecting in the x-axis then multiplies the entire function by $-1$, resulting in $-\sqrt{-x + 3}$.

Write an Equation for the Function That Is Described by the Given