ALGEBRA 2 6.0
CHAPTER 6
WITHOUT A CALCULATOR
You must be able to do the following for the this assessment
 Given two functions defined by algebraic expressions, determine the new
function obtained by taking the sum, difference, quotient, product or
composition of the two.
 Given a function h(x), determine two functions whose composition would
produce h(x).
 Determine the composition of two functions defined by ordered pairs.
 Find the domain for any function, including but not limited to
A set of ordered pairs
An algebraic expression such as
 Sum, difference, product or quotient of 2 functions
 Composition of functions (must show work using one of
the two methods shown in class)
 Given the graphs of two functions, f(x) and g(x), draw the graph of
f + g or f – g. Also be able to evaluate particular values, such as
fg(2) or (f – g)(3), by inspecting the graphs.
 Given a relation or function, find the inverse and determine whether the
inverse is a function.
 Determine the domain of the inverse of a function, recalling that the
domain of the inverse is the range of the original function.
 Given a graph sketch its inverse.
 Given a graph determine whether its inverse is a function, without
graphing, using the horizontal line test. Be able to explain the
significance of the horizontal line test.
 Given two functions determine whether they are inverses using
composition of functions (f(g(x)) = x and g(f(x))=x ).
 Solve a word problem whose solution requires the use of operations of
functions or inverses.
 Given a radical function (square root or cube root), identify the parent
function, domain, range, intercepts (if they exist), and transformations
from the parent function.
 Sketch a given radical function or inequality.
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Given a radical variable expression, state any restriction(s) needed for
the radical expression to represent a real number. (Remember
restrictions are NEVER needed when the index is odd, unless in a
fraction.)
Make sure simplified radical expressions meet these conditions:
o Absolute value ONLY WHERE NECESSARY (Remember absolute
value is NEVER needed when the index is odd.)
o Radicand as small as possible
o No radicals in denominators
o Index as small as possible
Rewrite radical expressions in exponential form.
Use Rules of Exponents to rewrite expressions involving rational
exponents.
Simplify expressions that include radicals and/or rational exponents.
Make sure simplified expressions using rational exponents meet these
conditions:
o No negative exponents
o No fractional exponents in the denominator
o No complex fractions
Find a sum, difference, product, or quotient of radicals
Solve three types of radical equations algebraically
o Variable does NOT appear in the radicand (you do NOT have to
square/cube both sides of the equation to solve these)
o Single radical, variable appears in the radicand (Must CHECK
answers)
o Two radicals, variable appears in the radicand (Must CHECK
answers)
Solve radical inequalities graphically. (Remember to consider the domain
of the radical in your final answer.)
Solve a word problem whose solution requires the use of a radical
function or inequality.
Solve a problem related to essential material from earlier in the year
(as mandated by the district).