Answer
$\text{(c)}$
Work Step by Step
In order to find the answer, we will have to recall the following about the graph of $y=f(x)$.
a) The graph of the function $y=-f(x)$ involves a reflection about the $x$-axis of the original function $f(x)$.
b) The graph of the function $y=f(-x)$ involves a reflection about the $y$-axis of the original function $f(x)$.
c) The graph of the function $y=f(x)+a$ defines a vertical shift of $|a|$ units upward when $a \gt 0$, and downward side when $a\lt 0$ of the original function $f(x)$.
d) The graph of $y=f(x-p)$ defines a horizontal shift of $|p|$ units to the right when $p \gt 0$, and to the left when $p \lt 0$ of the original function $f(x)$.
e) The graph of $y=k\cdot f(x)$ can be obtained a vertical stretch when $k\gt 1$ or compression when $0\lt k \lt1$) of the original function $f(x)$.
We will consider point $(e)$ that the resulting function involves a vertical stretch by a factor of $2$ units of the original function $f(x)$. So, the $y$-value of the function $y=2 f(x)$ becomes twice times the y-value of $y=f(x)$.
This implies that if $(1, 3)$ is on the graph of $y=f(x)$ will become $(1, 6)$ on the graph of $y=2f(x)$.
Therefore, the answer is Option (c).
