A function f is given, and the indicated transformations are applied to its graph (in the given order). Find the equation for the final transformed graph. $f ( x ) = \sqrt { x }$; shift 5 units to the left, stretch vertically by a factor of 2 , and reflect in the $x$-axis.
A) $f ( x ) = - 2 \sqrt { x } + 5$
B) $f ( x ) = - \frac { 1 } { 2 } \sqrt { x } - 5$
C) $f ( x ) = - 5 \sqrt { x - 2 }$
D) $f ( x ) = - \sqrt { 5 x - 2 }$
E) $f ( x ) = - 2 \sqrt { x + 5 }$

Question

Quizplus · Accepted Answer

The correct transformations in order are: shift 5 units to the left (which changes $x$ to $x + 5$), stretch vertically by a factor of 2 (which multiplies the function by 2), and reflect in the $x$-axis (which multiplies the function by -1). Therefore, the final equation is $f(x) = -2\sqrt{x + 5}$.

A Function F Is Given, and the Indicated Transformations Are f(x)=xf ( x ) = \sqrt { x }f(x)=x​

A Function F Is Given, and the Indicated Transformations Are $f ( x ) = \sqrt { x }$