FinalExamPracticeProblems
(alloftheseproblemshavesolutionsonpreviousreviews)
⎧3 − 2 x
x>0
1)Graph f (x) = ⎨
x≤0
⎩−x + 2
2)
If g(x) = x 3 − x then find the difference quotient:
g(x + h) − g(x)
h
3)Findthezeros(ifmultiplezerosstatethemultiplicity)of:
P(x) = 3x 3 + 11x 2 − 6x − 8 4)Sketchthegraphofthepolynomial: P(x) = x 3 + 2x 2 − 3x 2x 2
5)Discussanyasymptotesandsketchthegraphof F(x) = 2
x −1.
6)Findtheinverse f −1 (x) ANDverifyitistheinversefunction:
f (x) = x 2 + 4 x
7)Solve: log(4 − x) =
8)
x ≥ −2 log(x + 8) + log(2x + 13) 10 x + 10 − x
=8
Solve:
2
π⎞
⎛
9)Graphonefullperiodofthefollowing: y = −2 cos ⎜⎝ x + 3 ⎟⎠ + 3 1− sin x 1+ sin x
10)Verifytheidentity: 1+ sin x − 1− sin x = −4 sec x tan x 11)Solvetheequationforanswersintheinterval 0 ≤ x < 2π :
2 cos 2 x + 1 = −3cos x 12)Solvetheequationforanswersintheinterval 0 ≤ x < 2π :
sin 2x cos x + cos 2x sin x = 0 13)Findthefivefifthrootsof-1+i.Writeyouranswersinstandardformroundedto
thenearestthousandth.
!
14)Solvethetriangle: C = 98.4 , a = 141, b = 92.3 v
u
v
15) v = 6, 7 u = 3, 4 Findtheprojectionof onto andwrite asthesumof
thatvectorandanotherthatisperpendiculartoit.
5
16)Solveandwriteanswersintrigonometricform: x + 32i = 0 2
17)Sketchthefollowing: x = −y − 8y − 7 2
2
18)Findthepolarformof x + 2y = 16 (
)
19)Findthepolarcoordinatesof −4 2, 4 2 n
9
2
20) ∑ n 2 2i − 3in i=1
(
)