# Study of a parametric function I would like to study this function for x &#x2265;<!-- ≥ -->

Jordon Haley 2022-05-14 Answered
Study of a parametric function
I would like to study this function for $x\ge 0$, $\mathrm{\forall }b,d\in \mathbb{R}$:
$y=\frac{b+dx}{1-b-dx}$
Can I say that it is monotone increasing (decreasing) over x in its domain for $d>0$ ($d<0$)?
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Kharroubip9ej0
Step 1
Note that $\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left[\frac{b+dx}{1-b-dx}\right]=\frac{d}{{\left(1-b-dx\right)}^{2}}$
Step 2
and hence the function is monotone increasing (decreasing) for $d>0$ ($d<0$).
###### Not exactly what you’re looking for?
Dominick Blanchard
Explanation:
By the quotient rule we get after simplifications for the first derivative ${y}^{\prime }=\frac{d}{\left(dx+b-1{\right)}^{2}}$
Step 2
Now you can consider the cases $d>0$ or $d<0$