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Is $y=-\dfrac 12 f(x)$ equal to $-2y=f(x)$ and if so, does this indicate a vertical compression of $\dfrac 12$ and a reflection in the $y$-axis?

Grimestock
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    Yes and no. The reflection from the $-$ sign is in the $x$-axis – Henry Mar 14 '18 at 01:35
  • Thank you! So there is a vertical compression by a factor of 1/2 and a reflection in the x-axis? – Grimestock Mar 14 '18 at 01:37
  • Think about it this way: $-f(x)$ is negating the outputs of the function, so all the $y$-values are negated, thus its flipped over the $x$-axis. $f(-x)$ negates the input of the function, so first, all the $x$-values are negated, so its flipped over the $y$-axis. – Andrew Li Mar 14 '18 at 01:42

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$\dfrac 12f(x)$ is only a vertical compression of $f(x)$.

On the other hand, when you introduce the negative sign, $-\dfrac 12f(x)$ is a vertical compression, as well as a reflection over the $x$-axis!