Cheat sheet for Section 7.1

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Transcript Cheat sheet for Section 7.1

Section 7.1 Rational Functions
Cheat Sheet
𝑑
𝑦=
+𝑓
π‘₯+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:_____________________________
π‘₯ = βˆ’π‘’
Vertical Asymptote:______________
𝑦=𝑓
Horizontal Asymptote:___________
There is always a vertical and
horizontal asymptote.
Range:
β„œ, 𝑦 β‰  𝑓
________________
β„œ, π‘₯ β‰  βˆ’π‘’
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, π‘‘β„Žπ‘’ π‘“π‘’π‘›π‘π‘‘π‘–π‘œπ‘› 𝑖𝑠 𝑑𝑒𝑐. (βˆ’βˆž, βˆ’ 𝑒 (βˆ’π‘’, ∞
𝑖𝑓 𝑑 < 0, π‘‘β„Žπ‘’ π‘“π‘’π‘›π‘π‘‘π‘–π‘œπ‘› 𝑖𝑠 𝑖𝑛𝑐. (βˆ’βˆž, βˆ’ 𝑒 (βˆ’π‘’, ∞
Decreasing:____________________________
The function is either Increasing or Decreasing. It can’t be both