Compare the functions shown below:
h(x)
f(x) = 2 sin (3x + tt) - 2 g(x) = (x - 3)2 - 1
which function has the smallest minimum y-value?

h had the lowest because -6 is less than both -4 and -1.

Step-by-step explanation:

The range of is .

The range of is since the amplitude has been changed from 1 or 2. (It has been vertically stretched.)

The range of still had range because changing inside only effects the period and phase shift.

The range of would have range and after simplifying this you get the range is .

The smallest value obtained by function f is -4.

is a parabola in vertex form. The vertex is where the maximum or minimum of a parabola will occur.  It has a minimum since the coefficient of is positive.

Comparing to where the vertex is (h,k) we should see that the vertex of g is at (3,-1). So the lowest y obtain by this parabola is -1.

So g lowest y is -1.

h is a list of points.  All you have to do is look through the second column to see which y is the lowest.

The lowest y there is -6 because -6 is less than all the other y's they have listed.

h has the lowest.

g has the highest.