Answer
a) it is decreasing function
b)
x<0 it is increasing function
x>o it is decreasing function
c)
t < $-\frac{1}{2}$ it is decreasing function
t > $-\frac{1}{2}$ it is increasing function
d) it is increasing function
Work Step by Step
a)
f(x) = $3^{-x}$ = $(\frac{1}{3})^{x}$
base is less than 1 so it is decreasing function
b)
y = $\frac{1}{x^{2}+1}$
x<0 it is increasing function
x>o it is decreasing function
c)
y = $t^{2}+t$
y = $[t^{2}+2(t)(\frac{1}{2})+(\frac{1}{2})^{2}]-(\frac{1}{2})^{2}$
y = $[t+\frac{1}{2}]^{2}-\frac{1}{4}$
t < $-\frac{1}{2}$ it is decreasing function
t > $-\frac{1}{2}$ it is increasing function
d)
y = $t^{3}+t$
it is increasing function
