Always remember general rules of transformation.
1) Vertical Shift:
y= f(x)+k ; shifts the graph of f up k units if k>0, shifts it down |k| units if k<0.
2) Horizontal Shift:
y=f(x+h) ; shifts the graph of f left h units if h>0, shifts it right |h| units if h<0.
3) Reflection across x-axis
y= - f(x) ; reflect the graph of f across the x-axis.
Now,
The parent function is y= -(x+2)²
1. y= -(x+4)²
In this question +2 is added with x+2 and becomes y= -(x+2+2)²=-(x+4)²
So, according to rule 2 it will shift the parent function to the left by 2 units.
E is the correct option.
2. y = - (x + 2)² - 2
In this question, -2 is added to the parent function and we get y= - (x + 2)² - 2
So, according to rule 1, it will shift the graph down by 2 units.
F is the correct option.
3. y=(x - 2)²
In this question, two operations are performed on the parent function.
First one, -4 is added with x+2 so we get x+2-4= x-2
Second one, -1 is multiplied with parent function.
By performing the two operations at a time we get a new function which is
y=-(-(x+2-4)²)=(x-2)²
The first operation will translate the parent function 4 units right (according to rule 2).
The second operation will reflect the graph across x-axis(according to rule 3).
D and translation 4 units to right is correct option.
4. y= 2 -(x+2)²
In this question, we add +2 to the parent function so according to rule 1 it will shift the graph up by 2 units.
C is the correct option.
5. y= -x²
In this question, we add -2 to x+2 so we get a new function y= -(x+2-2)²=-x²
So, according to rule 2 it will shift the graph right by 2 units.
B is the correct option.
6. y= (x+2)²
In this question, -1 is multiplied with parent function and we get
y= -(-(x+2)²)= (x+2)²
So, according to rule 3 , graph is reflected across x-axis.
D is the correct answer.
The graph of parent function and question no. 1,2,3 are attached separately, while question no. 4,5,6 are attached in combined form(due to space limit).
