Compare the following functions: f(x) = 3 sin(x − π) + 4 g(x) graph of a quadratic with points at 1, 5 and 3, 1 and 5, 5 h(x) x y −2 4 −1 3 0 2 1 1 2 2 3 3 4 4 which function has the smallest minimum?

F(x), the minimum value occrurs at -1 because the min value of a sin function is -1 and it is multipiled by 3 so -3 is the min

g(x), we see (1,5) and (5,5). since we have the same y value, the axis of symmetry must be midway between the 2 x valuse
average of 1 and 5 is 3
so the x value of the vertex is 3
oh look, (3,1)
vertex is (3,1)
since (1,5) and (5,5) are both above (3,1), graphically speaking, (3,1) is the minimum, the minimum value of g(x) is 1

for h(x), there isn't really a clear equation,  (perhaps h(x)=|x-1|+1)
the minimum value is at (1,1). the value is 1

f(x) min is -3
g(x) min is 1
h(x) min is 1

f(x) has the smallest minimum value