Answer
a) $(-2, -2)$
b) $(3, -5)$
c) $(-1, 3)$
Work Step by Step
$(1,3)$ is a point on the graph of $y = f(x)$
this means $f(1) = 3$
(a) What point is on the graph of $y = f(x + 3) - 5$?
$x+3 = 1$
$x = -2$
For $x = -2$, y becomes
$y = f(-2+3)-5 = f(1)-5 = 3-5 = -2$
So, $(-2, -2)$ is on the graph
(b) What point is on the graph of $y = - 2f(x - 2) + 1$
$x-2 = 1 => x = 3$
For $x = 3$, we get
$y = -2f(1) +1 = -2\times3 + 1 = -5$
So, $(3, -5)$ is on the graph
(c) What point is on the graph of y = f(2x + 3)?
$2x + 3 = 1 => x =-1$
For $x =-1$, we get $y$
$y = f(1) = 3$
So point $(-1, 3)$ is on the graph