Answer
(a) $x = t-3$
$y = \frac{2}{t-3}$
(Note that $t \neq 3$)
We can see the graph below.
(b) $y = \frac{2}{x}$
$x\neq 0$
Work Step by Step
(a) $x = t-3$
$y = \frac{2}{t-3}$
$t \neq 3$
t = -1:
$x = (-1)-3 = -4$
$y = \frac{2}{(-1)-3} = -\frac{1}{2}$
t = 0:
$x = (0)-3 = -3$
$y = \frac{2}{(0)-3} = -\frac{2}{3}$
t = 1:
$x = (1)-3 = -2$
$y = \frac{2}{(1)-3} = -1$
t = 2:
$x = (2)-3 = -1$
$y = \frac{2}{(2)-3} = -2$
$t = \frac{5}{2}$:
$x = (\frac{5}{2})-3 = -\frac{1}{2}$
$y = \frac{2}{(\frac{5}{2})-3} = -4$
$t = \frac{7}{2}$:
$x = (\frac{7}{2})-3 = \frac{1}{2}$
$y = \frac{2}{(\frac{7}{2})-3} = 4$
t = 4:
$x = (4)-3 = 1$
$y = \frac{2}{(4)-3} = 2$
t = 5:
$x = (5)-3 = 2$
$y = \frac{2}{(5)-3} = 1$
t = 6:
$x = (6)-3 = 3$
$y = \frac{2}{(6)-3} = \frac{2}{3}$
t = 7:
$x = (7)-3 = 4$
$y = \frac{2}{(7)-3} = \frac{1}{2}$
We can see the graph below.
(b)
$x = t-3$
$y = \frac{2}{t-3}$
Therefore: $~~y = \frac{2}{x}$
Since $t \neq 3$, then $x\neq 0$
