Answer
(a) As x increases, $f(x)$ increases. Example: $f(x)=x$
(b) As x increases, $f(x)$ decreasses. Example: $f(x)=-x.$
(c) As x increases, $f(x)$ neither increases nor decreases. Example: $f(x)=2$
Work Step by Step
(a) As x increases, an increasing function will increase as well.
Algebraically: $\quad x_{1} < x_{2} \Rightarrow f(x_{1}) < f(x_{2})$
( the function value is greater the greater argument ,$ x_{2}$)
Example: $f(x)=x$
The greater x gets, the greater x gets (the greater f(x) gets).
(b) As x increases, a decreasing function will decrease .
Algebraically: $\quad x_{1} < x_{2} \Rightarrow f(x_{1}) > f(x_{2})$
( the function value is smaller for the greater argument ,$ x_{2}$)
Example: $f(x)=-x$
The greater x gets, the smaller $-x$ gets (the smaller f(x) gets).
(c) As x increases, a constant function neither increases nor decreases .
Algebraically: $\quad x_{1} < x_{2} \Rightarrow f(x_{1}) = f(x_{2})$
( the function value is unchanged for the greater argument ,$ x_{2}$)
Example: $f(x)=2$
The function value is unchanged, equals 2 regardless of x.
