Match each function formula with the corresponding transformation of the parent function y = (x - 1)2 1. y = - (x - 1)2 Reflecte
d over the y-axis 2. y = (x - 1)2 + 1 Reflected over the x-axis 3. y = (x + 1)2 Translated right by 1 unit 4. y = (x - 2)2 Translated down by 3 units 5. y = (x - 1)2 - 3 Translated up by 1 unit 6. y = (x + 3)2 Translated left by 4 units
Since you have studied transformations, you are familiar with the effect of different modifications of the parent function:
f(x-a) . . . translates right by "a" units
f(x) +a . . . translates up by "a" units
a·f(x) . . . vertically scales by a factor of "a". When a < 0, reflects across the x-axis
f(ax) . . . horizontally compresses by a factor of "a". When a < 0, reflects across the y-axis.
Note that in the given list of transformed functions, there is one that is (x+1)². This is equivalent to both f(x+2) and to f(-x). The latter is a little harder to see, until we realize that (-x-1)² = (x+1)². That is, this transformed function can be considered to be either a translation of (x-1)² left by 2 units, or a reflection over the y-axis.
