Find h(t) + k(t) if h(t) = {(-4,5), (-2,-3), (0,5), (1,3), (3,-1), (5,5)} and
k(t) = {(-3,-2), (-2,6), (-1,0), (1,0), (2,-6), (3,5), (4,0), (6,-2)}.
To find h(t) + k(t), we need to add the corresponding points in the two functions.
First, let's represent h(t) and k(t) as sets of points:
h(t) = {(-4,5), (-2,-3), (0,5), (1,3), (3,-1), (5,5)}
k(t) = {(-3,-2), (-2,6), (-1,0), (1,0), (2,-6), (3,5), (4,0), (6,-2)}
Now, let's add the corresponding points together:
h(t) + k(t) = {((-4,5) + (-3,-2)), ((-2,-3) + (-2,6)), ((0,5) + (-1,0)), ((1,3) + (1,0)), ((3,-1) + (2,-6)), ((5,5) + (3,5)), ((5,5) + (4,0)), ((5,5) + (6,-2)))}
Adding each pair of points:
((-4,5) + (-3,-2)) = (-7,3)
((-2,-3) + (-2,6)) = (-4,3)
((0,5) + (-1,0)) = (-1,5)
((1,3) + (1,0)) = (2,3)
((3,-1) + (2,-6)) = (5,-7)
((5,5) + (3,5)) = (8,10)
((5,5) + (4,0)) = (9,5)
((5,5) + (6,-2)) = (11,3)
Therefore, h(t) + k(t) = {(-7,3), (-4,3), (-1,5), (2,3), (5,-7), (8,10), (9,5), (11,3)}