Question

Match each function formula with the corresponding transformation of the parent function y=-x2-1.

Reflected across the y-axis
Translated right by 1 unit
Translated down by 1 unit
Translated up by 1 unit
Reflected across the x-axis
Translated left by 1 unit
1. y=-x2-1
2. y=-(x - 1)2 - 1
3. y= x2 +1
4. y=-x2
5. y=-(x+ 1)2 - 1
6. y=-x2 - 2

Answer 1

Your answer will be #2. y=-(x-1)2-1

Answer 2

Answer:

Since, when a function f(x) is reflected across x-axis then resultant function is -f(x), and reflected across y-axis then resultant function is f(-x),

Also, In translation of f(x),

If the transformed function is,

g(x) = f(x+a)

If a is positive then function is shifted a unit left,

If a is negative then function is shifted a unit right,

While, if transformed function is,

g(x) = f(x) + a

If a is positive then function is shifted a unit up,

If a is negative then function is shifted a unit right,

Here, the given parent function is,

$y=-x^2-1$

Hence, by the above explanation we can match the unction formula with the corresponding transformation, shown below,

1. $y=-x^2-1$  : Reflected across the y-axis

2. $y=-(x - 1)^2 - 1$  : Translated right by 1 unit

3. $y= x^2 +1$ : Reflected across the x-axis

4.$y=-x^2$  : Translated up by 1 unit

5. $y=-(x+ 1)^2 - 1$  : Translated left by 1 unit

6. $y=-x2 - 2$  : Translated down by 1 unit