Question

Write a function formula for g using the function f.

Answer 1

Answer:

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

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

Step-by-step explanation:

Transformations

Function f can be obtained by knowing function g and vice-versa.

Suppose we know the expression of function f. If we reflect f across the x-axis, we get function g but displaced 3 units to the right.

Thus, we only have to translate the reflected f 3 units to the left:

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

Similarly, if g(x) is reflected across the x-axis and translated by 3 units to the right, we get f(x), thus:

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