Answer
See below.
Work Step by Step
Taking any two values $x_{1}$ and $x_{2}$ from the domain of $f$, where $x_{1}\lt x_{2}$, we have:
if it is always the case that $f(x_{1})\lt f(x_{2})$, (for any choice of $x_{1}$ and $x_{2}$, where $x_{1}\lt x_{2}$), then the function is an increasing function.
(The function value of a greater input is always greater. The function values increase as the inputs increase.)
If, on the other hand, it is always the case that $f(x_{1})\gt f(x_{2})$, (for any choice of $x_{1}$ and $x_{2}$, where $x_{1}\lt x_{2}$), then the function is a decreasing function. (The function value of a greater input is always smaller. The function values decrease as the inputs increase.)
Examples:
$f(x)=-x \quad$ is a decreasing function.
(Take any two inputs. The function value of the greater input is less than the function value of the smaller input.
For example, $f(2)=-2$ is greater than $f(3)=-3)$.
$ f(x)=x+1\quad$ is an increasing function.
(The function value of a greater input is always greater
For example, $f(2)=3$ is less than $f(3)=4)$
$f(x)=2^{-x} \quad$ is a decreasing function
(For example, $f(2)=2^{-2}=\displaystyle \frac{1}{4}$ is greater than $f(3)=2^{-3}=\displaystyle \frac{1}{8})$
$f(x)=2^{x} \quad$ is an increasing function
(For example, $f(2)=2^{2}=4$ is less than $f(3)=2^{3}=8)$
