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

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

(a)

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

(b)

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

(c)

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

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