which results only in a horizontal compression of $y = \\frac{1}{x}$ by a factor of 6?\n$y =…

which results only in a horizontal compression of $y = \\frac{1}{x}$ by a factor of 6?\n$y = \\frac{1}{6x}$\n$y = -\\frac{1}{6x}$\n$y = \\frac{6}{x}$\n$y = -\\frac{6}{x}$

which results only in a horizontal compression of $y = \\frac{1}{x}$ by a factor of 6?\n$y = \\frac{1}{6x}$\n$y = -\\frac{1}{6x}$\n$y = \\frac{6}{x}$\n$y = -\\frac{6}{x}$

Answer

Explanation:

Step1: Recall horizontal - compression rule

For a function $y = f(x)$, a horizontal compression by a factor of $a$ ($a>0$) is given by the transformation $y = f(ax)$. For the function $y=\frac{1}{x}$, if we want a horizontal compression by a factor of 6, we replace $x$ with $6x$. So the new function is $y=\frac{1}{6x}$. The negative - sign in front of the function would reflect it over the $x$ - axis, and a constant multiplier in the numerator other than 1 would change the vertical stretch or compression.

Answer:

$y = \frac{1}{6x}$ (corresponding to the first option)