Answer
(a)
$$
f(x)=5
$$
This function is a horizontal line and has slope $0$ the derivative is $0$.
(b)
$$
f(x)=x
$$
This function has slope 1 the derivative is 1.
(c)
$$
f(x)=-x
$$
This function has slope -1 the derivative is -1.
(d)
$$
f(x)=3
$$
This function is vertical line and has undefined slope the derivative does not exist.
(e)
$$
f(x)=mx+b
$$
This function has slope $m $ the derivative is $m$.
Work Step by Step
(a)
$$
f(x)=5
$$
This function is a horizontal line and has slope $0$ the derivative is $0$.
(b)
$$
f(x)=x
$$
This function has slope 1 the derivative is 1.
(c)
$$
f(x)=-x
$$
This function has slope -1 the derivative is -1.
(d)
$$
f(x)=3
$$
This function is vertical line and has undefined slope the derivative does not exist.
(e)
$$
f(x)=mx+b
$$
This function has slope $m $ the derivative is $m$.
