y-intercept of odd function

Question

f(x) is an odd function and f(4)= -11

If g(x)=3f(x-4)+5 ,then what is the y-intercept of g(x)

Answer 1

An Odd function is one that has this property: f(-x) = -f(x).

Since f(x) is an odd function and f(4) = -11, then f(-4) = -f(4) = -(-11) = 11.

The y-intercept of g is simply g(0):

g(x) = 3f(x-4) + 5

g(0) = 3f(-4) + 5

= 3(11) + 5

= 38, ans.