Section 7.1 Rational Functions
Cheat Sheet
𝑑
𝑦=
+𝑓
𝑥+𝑒
Parent Function:______________________
The parameters
must
d:__________
have
don’t need
e: __________
don’t need
f: __________
Points for the Must have at least 4 points on each
side of the vertical asymptote
function:_____________________________
𝑥 = −𝑒
Vertical Asymptote:______________
𝑦=𝑓
Horizontal Asymptote:___________
There is always a vertical and
horizontal asymptote.
Range:
ℜ, 𝑦 ≠ 𝑓
________________
ℜ, 𝑥 ≠ −𝑒
Domain: ________________
Set x=0 and solve. If there is no e,
then there is no y-intercept
Y-intercept:_______________________________
This is the same thing
as an x-intercept.
You can use the trace
feature on your calc
to approximate
Find the
Set y=0 and solve. You will have to cross multiply to solve for x.
Zero(s):________________________________
If there is no parameter f, there
is no zero.
Increasing or 𝑖𝑓 𝑑 > 0, 𝑡ℎ𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑖𝑠 𝑑𝑒𝑐. (−∞, − 𝑒 (−𝑒, ∞
𝑖𝑓 𝑑 < 0, 𝑡ℎ𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑖𝑠 𝑖𝑛𝑐. (−∞, − 𝑒 (−𝑒, ∞
Decreasing:____________________________
The function is either Increasing or Decreasing. It can’t be both