Name:______________________________________________
1
APCalculusAB&BC–page
ThefollowingareskillsyoushouldhavemasteredinPre-CalculusandAlgebraIIwith
Trig.Manyitemsrequireacalculator.Duefirstdayofclassforaclassworkquiz
grade.
ChartofBasicGraphs
Sketchthegraphofeachandidentifytherequesteditems.
CONSTANT
y=constant
y = -2 LINEAR
y=mx+b
Domain
Range
Domain
Range
CUBIC
y=x3
1
f ( x) = ( x - 1) 2 - 2 2
Domain
Range
Domain
Range
RADICAL(SquareRoot)
y= 𝒙
Domain
Range
-1
y = x + 3
2
QUADRATIC
y=ax2+bx+cy=a(x-h)2+k
CUBEROOT
𝟑
y= 𝒙
Domain
Range
Name:______________________________________________
“SEAGULL”
y=x2/3
ABSOLUTEVALUE
y=|x|
Domain
Range
RATIONAL
y=p(x)/q(x)
Domain
Range
x -1
y=
x +1
Domain
Range
GREATESTINTEGER
y=[x]ory=[[x]]
NATURALLOG
y=lnx
Domain
Range
2
APCalculusAB&BC–page
Domain
Range
EXPONENTIAL
y=ex
Domain
Range
Name:______________________________________________
SineFunction
y = sin x CosineFunction
y = cos x Domain
Range
TangentFunction
y = tan x Domain
Range
Domain
Range
Exactvaluesoftrigfunctions
p
6
sin q cos q tan q csc q sec q cot q p
3
p
4
sin q cos q tan q csc q sec q cot q q=
q=
q=
q =0 p
q= 2
q =p 3p
q= 2
3
APCalculusAB&BC–page
Name:______________________________________________
APCalculusAB&BC–page
Ë PIECEWISEFUNCTIONS
Apiecewisefunctionisasetofoneormorefunctionsdefinedoverspecifieddomainvalues.
Sinceapiecewisefunctionisafunction,itmustpasstheverticallinetest.
STEPSINGRAPHINGAPIECEWISEFUNCTION
1.Makeatableofvaluesusingthespecifiedxvalues
2.Plotthepointsanddecideifthemajorpointisopen(hole)orclosed(regularpoint)
3.Checktomakesurethatyourgraphpassestheverticallinetest
Grapheachpiecewisefunction.
−𝑥 ' + 4,𝑥 ≤ −2
1.𝑓 𝑥 = .
𝑥 + 3,𝑥 > −2
'
𝑥 . ,𝑖𝑓𝑥 < 1
3.𝑓 𝑥 = −2,𝑖𝑓𝑥 = 1
𝑥 ,𝑖𝑓𝑥 > 1
1
− 𝑥 + 1,𝑥 ≤ 2
'
2.𝑓 𝑥 = 2,2 < 𝑥 ≤ 4
𝑥,𝑥 > 4
4
Name:______________________________________________
Review(GraphingandTrig)Worksheet Graphthefollowingfunctionsandanswerthequestions.
1.𝑓 𝑥 = 𝑥 + 1 − 2
2.𝑓 𝑥 = 𝑒 67 APCalculusAB&BC–page
5
3.𝑓 𝑥 = −ln(𝑥)
Domain:___________________________ Domain:___________________________ Domain:_______________________
Range:_____________________________ Range:_____________________________ Range:_________________________
Vertex:___________
x-intercept:______________
Equationofasymptote:__________ Eq.ofAsymptote:_____________
y-intercept:______________
|7|
4.𝑓 𝑥 = − 2𝑥 − 3 + 1
5.𝑓 𝑥 = 6.𝑓 𝑥 = −𝑥 '/. 7
Domain:___________________________ Domain:___________________________ Domain:_______________________
Range:_____________________________ Range:_____________________________ Range:_________________________
Vertex:___________
x-intercept:______________
y-intercept:______________
Name:______________________________________________
APCalculusAB&BC–page
6
7.Thegraphshowstwolinesthatareparallel.Writetheequationof
eachlineandcomparetheslopes.Writeageneralstatementaboutthe
slopesofparallellines.
8.Thegraphshowstwolinesthatareperpendicular(meetataright
angle).Writetheequationofeachlineandcomparetheslopes.Writea
generalstatementabouttheslopesofperpendicularlines.
Graphthepiecewisefunction.
9.𝑓 𝑥 =
𝑒 7 ,𝑥 > 0
1
− 𝑥 − 2, 𝑥 ≤ 0
'
10.
𝑥,0 < 𝑥 < 4
11.𝑔 𝑥 = −2𝑥,𝑥 ≤ 0 5,𝑥 = 4
Name:______________________________________________
APCalculusAB&BC–page
Writetheequationofthepiecewisefunction.
12.
13.
7
14.
Whatarethesidesofthefollowingspecialrighttriangles?
15. 16.
60˚
x
45˚
y
z
z
45˚
30˚
x
y
x=________y=_________z=_________ x=________y=_________z=_________
Findtheexactvalueofeachtrigfunctiongiventheangle.
sinθ
cosθ
tanθ
cscθ
secθ
cotθ
B
17.𝜃 = C
.B
18.𝜃 = D
19.𝜃 = 0
B
20.𝜃 = − .
21.UsingaGraphingCalculatorfindtherelativemaxes,relativemins,andallx-interceptstothree
decimalplaces𝑦 = 2𝑥 D + 𝑥 . − 6𝑥 ' − 4
22.Usingacalculatordeterminetheintersection(s)ofthepolynomialinQuestion21andthecurve
𝑦 = 𝑒 7 − 2tothreedecimalplaces.