Answer:
Option: C is the correct answer.
The equation of the Blue graph is:
C. [tex]G(x)=(x+3)^2[/tex]
Step-by-step explanation:
We are given a graph of a parent function F(x) as:
[tex]F(x)=x^2[/tex]
We know that the function G(x) is nothing but a translation transformation of the parent function by some units to the left.
Also we know that the transformation k units to the left or right is denoted by:
F(x) → F(x+k)
if k>0 then the shift is k units to the left.
and if k<0 then the shift is k units to the right.
Here we have k= 3 and shift is to the left.
Hence, the equation of translated function is:
G(x)=F(x+3)
i.e. [tex]G(x)=(x+3)^2[/tex]
