Question

Write a function formula for g using the function f.g(x)=Write a function formula for f using the function g.f(x)=

Answer 1

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:

$g(x)=-f(x+3)$