Both the functions shown (blue and red) are parabolas.
g is a transformation f the function f.
We have to figure out the transformation and write the equation of g with respect to f.
g is (with respect to the function f):
• reflected upside down [reflected about x-axis]
,
• translated 3 units left
Reflection with respect to x-axis makes the function negative, so:
f(x) would be -f(x)
Then,
Translation "a" units to the left, makes a function f(x) into f(x+a), thus:
f(x) would be -f(x+3)
This is the function g. Thus we can say:
