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Pre-Calculus Flash Drill
See if you can identify the function that probably goes with each of these simple
graphs….
lyrespective
xxf
and
xxf
)(
)( 2
How about these?
lyrespective
xxf
and
xxf
3
3
)(
)(
What about this one?
2
2
xxf 1tan)(
Did you know it?
You are a tiger!
How about these?
xxf
1)(
and222 ryx
respectively
and finally:
lyrespective
xxf
and
exf x
ln)(
)(
Define an
Even Function
)()( xfxf
Note: It is NOT enough to know the graph is
symmetric with respect to the y-axis.
Define an
Odd Function
)()( xfxf Again, please note that it is NOT enough to know that the graph has origin
symmetry.
The graph of x = a
is…
… a vertical line.
The graph of y = a
is…
… a horizontal line.
OK…that’s enough about graphs!
Let’s move on…
?1 x
x
1
?2/1 x
x
?2 x
2
1
x
?n mx
nm
x
?ln nx
xn ln
?ln xy
yx lnln
?ln y
x
yx lnln
?
?log xb
b
x
ln
ln
?1
ln
x
xln
?1ln
0
?ln xe
x
?ln xe
x
OK…enough of the logs already!
The formula for the slope of a
line is
m = ?
12
12
xx
yy
x
y
Point slope equation of a
line ?
)( 11 xxmyy
Midpoint Formula = ?
2,
22121 yyxx
Distance Formula=?
212
212 )()( xxyy
Here comes your favorite thing!
Yeah! Trigonometry!
?0sin
0
?0cos
1
?6
sin
2
1
?4
sin
2
2
2
1or
?3
sin
2
3
?2
sin
1
?2
cos
0
?3
cos
2
1
?4
cos
2
2
2
1or
?6
cos
2
3
?cos
1
?0tan
0
?4
tan
14
sin4
cos
because:
?2
tan
(or undefined)
?3
tan
3
?6
tan
3
1or
3
3
?2
1sin 1
6
?2
1cos 1
4
3
?2
3sin 1
3
?1tan 1
sine and cosine have to be equal!
4
?3tan 1
3131
0
31
13
Answer:3
OK…now let’s see if you know your identities!
?cossin 22 xx
1I hope you knew that one!!!
?tan1 2 x
x2sec
?1sec2 x
x2tan
?sincos 22 xx
x2cos
?2sin x
xx cossin2This one is very important!!
Now for a little algebra and you’ll be done!!
?22 ba
baba
?33 ba
22 bababa
Notice there is NO “2”
?33 ba
22 bababa
Still no 2!
?)( 2 ba
Last one…
22 2 baba There’s that two you wanted before!
If you know all this material, then you are prepared to begin
calculus… All you need now is a sharp mind, a sharp pencil and
a really big eraser!
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