Answer
a) $(-4, 2)$
b) $(1, -12)$
c) $(-4, 5)$
Work Step by Step
$(-3, 5)$ is a point on the graph of $y = g(x)$.
Which means $g(-3) = 5$
(a) What point is on the graph of $y = g(x + 1) - 3$
$x+1 = -3 => x = -4$
For $x = -4$, we get
$y = g(-3) -3 = 5 - 3 = 2$
So, $(-4, 2)$ is on the graph
(b) What point is on the graph of $y = - 3g(x - 4) + 3$?
$x-4 = -3 => x = 1$
For $x = 1$, we get
$y = -3g(-3) + 3 = -15 + 3 = -12$
So, $(1, -12)$ is on the graph
(c) What point is on the graph of $y = g(3x + 9)$?
$3x+9 = -3 => x = -4$
For $x = -4$, we get
$y = g(-3) = 5$
So, $(-4, 5)$ is on the graph
