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# A function $y = f(x)$ is transformed to the function $y = -f(-x)=g(x):$ a. Describe the nature of the transformation. b. If (3, -7) lies on $y = f(x),$ find the transformed point on g(x). c Find the point on $f(x)$ that transforms to the point (-5, -1).

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The function $y = f(x)$ is transformed to the function $y = - f(- x) = g(x)$

#### (a)

The function is reflected twice; once on the $x$-axis, and once on the $y$-axis. this will cause the function to rotate $180\text{\textdegree}$ about the origin.

#### (b)

The original point $(3, -7)$ on $y = f(x)$ will have the image point $(- 3, 7)$ on $g(x)$; the opposite signs of both $x$, and $y$ coordinates.

#### (c)

The image point $(- 5, - 1)$ on $g(x)$ corresponds to the original point $(5, 1)$ on $y = f(x)$; the opposite signs of both $x$, and $y$ coordinates.

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