Answer
a) The new point is $(3,1)$.
b) The new point is $(-2,-4)$.
c) The new point is $(6,-6)$.
Work Step by Step
(a) The translation $f(x)+5$ moves the graph up 5 units. The $x$-coordinate is not changed, but the $y$-coordinate is $-4+5=1$. The new point is $(3,1)$.
(b) The translation $f(x+5)$ shifts the graph to the left 5 units. The $y$-coordinate is not changed, but the $x$-coordinate is $3-5=-2$. The new point is $(-2,-4)$.
(c) This translation shifts both the $x$ and $y$ coordinates, 3 units right and 2 units down, resulting in $(6,-6)$.
