Given #-f(x)#, how do you describe the transformation?

1 Answer
Geoff K.
Dec 31, 2016

A reflection about the #x#-axis.

Explanation:

For any function #f#, its output at any given input #x# is just #f(x)#.

When we take that output #f(x)# and make it negative (i.e. #-f(x)#), we're just flipping the sign of the output—positives become negatives, and vice versa.

Let's say that when #x=3,# we have #f(x)=5#.
Thus, when #x=3,# we have #"-"f(x)="-"5#.

All that happens is the sign of the output value changes—points that were once above the #x#-axis are now below, with no shift left or right.

This is simply stated as a reflection where the mirror is the #x#-axis, also called a reflection about the #x#-axis.

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