Final Exam Review Topics
Simplify radicals and exponential expressions
Simplify a rational expression
Model a linear equation.
Finding the equation of a circle and locating the radius and center and visa versa.
Operations (+ * - /) on complex numbers and negative square roots
Solve the equation
 linear
 lbs value
 quadratic
 rational
 radical
 third degree with factoring
 fourth degree
Functions:
 domain of equation
 domain and range of graph
 vertical line test
 combining functions such as +, -, *, / . Finding
functions, values and domain
 composition: find values and function in x.
 one-to-one functions – horizontal line test
 finding the inverse algebraically and graphically
 simplify difference quotient
Given a graph
 intervals of increase and decrease
 intervals >, <,  ,  0 for quadratic and rational
inequalities
 finding g(a) , f(a), and find x given g(b), etc
 local minima and maxima
 degree
 positive negative
 x-intercepts – recognize behavior and find
multiplicity
 y- intercept
 find power function
 write function of graph in factored form
 horizontal and vertical asymptotes
Piecewise functions
 find f(a), and x given f(a) for both graphs and
function equations
 graph a piecewise function
 given a graph
o find the domain
o find the piecewise functions describing
the graph
Given a factored function find:
 degree
 positive negative
 x-intercepts – recognize behavior and find
multiplicity
 y-intercept
 find power function
Rational functions
 Solve inequality using test points
 Find vertical and horizontal asymptotes
 Find x- and y-intercepts
 Graph rational function
Quadratic functions: Find the following from a graph or
function.
 Find vertex
 x- and y-intercepts
 concavity
 graph a quadratic with above characteristics
Quadratic word problems (revenue, height, etc)
 maximum or minimum (vertex)
 x-and y-intercepts
Transformations
 List all transformations given a function in
terms of g(x) (ex:  2  g ( x  2) )
 List transformations given a graph
 List transformations and be able to graph
o quadratic
o absolute value
o cubic
o square root
o exponential
o logarithm
Exponential functions
 write as a log
 graph using transformations
 solve and exponential equation
 word problems: set up a exponential growth
function and find t, k, A(t), etc.

Logarithms
 graph using transformations
 write as an exponential expression
 simplify an expression without a calculator
 combine multiple logs (ln) into one log using
three log properties
 separate single log into more than one log using
log (ln) properties
 change of base formula for log or ln
 use log (ln) properties to simplify log equation