compared with the graph of the parent function, which equation shows a vertical stretch by a factor of 6, a…

compared with the graph of the parent function, which equation shows a vertical stretch by a factor of 6, a shift of 7 units right, and a reflection over the x - axis?\n$y = 6\\sqrt{x + 7}$\n$y=-\frac{1}{6}\\sqrt{x - 7}$\n$y = 6\\sqrt{x}+7$\n$y=-6\\sqrt{x - 7}$\ndone

compared with the graph of the parent function, which equation shows a vertical stretch by a factor of 6, a shift of 7 units right, and a reflection over the x - axis?\n$y = 6\\sqrt{x + 7}$\n$y=-\frac{1}{6}\\sqrt{x - 7}$\n$y = 6\\sqrt{x}+7$\n$y=-6\\sqrt{x - 7}$\ndone

Answer

Explanation:

Step1: Recall transformation rules

For a parent - function $y = f(x)$, a vertical stretch by a factor $a$ gives $y = af(x)$, a shift $h$ units to the right gives $y = f(x - h)$, and a reflection over the $x$ - axis gives $y=-f(x)$.

Step2: Analyze each transformation for the square - root parent function $y=\sqrt{x}$

A vertical stretch by a factor of 6 gives $y = 6\sqrt{x}$. A shift of 7 units to the right changes it to $y = 6\sqrt{x - 7}$. A reflection over the $x$ - axis makes it $y=-6\sqrt{x - 7}$.

Answer:

$y=-6\sqrt{x - 7}$ (the fourth option)