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```Algebra III/Trigonometry Honors
Final Exam Study Guide
Ch 2: Functions
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Graph piecewise functions
Evaluate functions, add, subtract , multiply, and divide functions
Find the domain and range of functions
Find the inverse of a function and the restricted domain
Find the difference quotient
Find the intervals where a function is increasing, decreasing, or constant
Solve word problems involving linear functions
Graph functions using transformations
Ch 3: Polynomial Functions
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Graph polynomial functions including cubic functions
Find the zeros of a polynomial functions
Use the rational root theorem to find all possible rational roots of a polynomial function.
Ch 4: (sections 4.1, 4.2) Rational Functions
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Graph rational functions
Identify any asymptotes (horizontal, vertical, slant)
Find the domain and range of rational functions
Ch 5: Exponential and Logarithmic Functions
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Graph exponential and logarithmic functions and give the equations of the asymptotes
Write logarithmic equations in exponential form and vice versus
Expand and Condense logarithmic expressions
Solve exponential and logarithmic equations
Find the domain and range of exponential and logarithmic functions
Solve word problems involving exponential equations
Ch 6 Trigonometry
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Determine the trigonometric functions given a point on the terminal side of the angle
Solve word problems with trigonometric equations
Graph trigonometric functions
Solve trigonometric equations
Find the six trigonometric functions given an angle on the unit circle
Convert angles from degrees to radians and vice versus
Convert angles from degrees, minutes, seconds to decimal degrees and vice versus
Ch 7 Trigonometric Identities
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Verify trigonometric identities
Determine the other 5 trigonometric function values of an angle, given one trigonometric
function of the angle
Ch 8: Law of Cosines and Law of Sines, and Area of a triangle
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Use the laws of cosines and sines to solve a triangle
Solve word problems using the laws of cosines and sines
Find the Area of a triangle using A = 1/2bcsinA or Heron’s Formula
Ch 9: Systems of Equations
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Solve a non-linear system by graphing or substitution
Solve a linear system by graphing, substitution, or elimination(linear combination)
Solve word problems involving linear systems
Solve a 3x3 linear system algebraically and using the matrix feature on the calculator
Find the maximum value of a linear programming problem by graphing the constraints
and finding the corners.
Ch 11: Sequences and Series
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Find the nth term in an arithmetic, geometric, or recursive sequence.
Find a formula for the nth term in an arithmetic, geometric, or recursive sequence.
Find the sum of a finite arithmetic series or a finite or infinite geometric series
Use sigma notation to write a series
Formulas to memorize:
f ( x  h)  f ( x )
h
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Difference Quotient:
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Change to exponential form from logarithmic form and vice versus: log b x  y  b y  x
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Vertex Form: y  a( x  h)2  k vertex is (h, k)
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Possible rational roots for a polynomial function: qxn + ….. + p
roots are found by: ±factors of p divided by factors of q
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SOHCAHTOA
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Law of Sines:
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Law of Cosines: c 2  a 2  b 2  2ab cos C
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Area of a Triangle:
the possible rational
sin A sin B sin C
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a
b
c
SAS:
1
bc sin A
2
SSS:
s(s  a)(s  b(s  c) ,
s
log x MN  log x M  log x N
M
 log x M  log x N
N
log x M k  k log x M
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Properties of Logarithms: log x
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 r
Compound Interest Formula: A  P  1  
 n
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Continuous Compound Interest Formula: A  Pe rt
nt
1
a  b  c
2
```
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