Question

Match each function formula with the corresponding transformation of the parent function y = (x - 1)2 1. y = - (x - 1)2 Reflected 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

Answer 1

1. y = -(x-1)² . . . . reflected over the x-axis
2. y = (x-1)² +1 . . . . translated up by 1 unit
3. y = (x+1)² . . . . reflected over the y-axis
4. y = (x-2)² . . . . translated right by 1 unit
5. y = (x-1)² -3 . . . . translated down by 3 units
6. y = (x+3)² . . . . translated left by 4 units

Explanation:

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.