Review

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Math 140
Exam 2
Review
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Chapter 3
Recognize a graph as belonging to one of the
function families whose portraits appear in the
introduction. Determine precisely how
modifications to a function will affect its
graph. Recognize even or odd functions by graph
or formula Find the algebraic formula for the
composition of two functions. Work backward from
a composite function to find simpler functions
that produced it. Determine the domain of a
composite function. Determine from a graph
whether it is one-to-one and thus has an
inverse. Given the graph of a one-to-one
function, sketch the graph of the inverse
function. Given algebraic formulas for two
functions, test whether or not they are
inverses. Find the algebraic formula for the
inverse of a function. Know the relationship
between domain/range of a function and
domain/range of its inverse.
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Chapter 4
Apply the laws of exponents to algebraic
expressions (4.1) Write exponential models
(4.1) Approximate an instantaneous rate of
change, the slope of a curve at a point
(4.2) Convert exponential functions from standard
form to base-e form and vice-versa (4.2) Use a
logarithm scale to rescale data that vary widely
in magnitude (4.3) Translate exponential
statements into logarithmic statements
(4.3) Sketch graphs of logarithmic functions
(4.3) Use the definition and the properties of
logarithms to simplify expressions containing
logarithms (4.3, 4.4) Use logarithms in solving
equations (4.3, 4.4) Given a logistic model, find
and interpret its point of inflection and its
carrying capacity (4.5)
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Chapter 5
Sketch a graph of any quadratic function. This
includes locating any intercepts and finding the
coordinates of the vertex (5.1) Approximate the
instantaneous rate of change of a function at a
point (5.1) Interpret the coordinates of the
vertex of a parabola in the context of an
optimization problem (5.1) Find the zeros of a
polynomial function (5.2) Determine the global
behavior of a polynomial function (5.2) Find the
vertical asymptotes of a rational function
(5.3) Find the horizontal asymptotes of a
rational function (5.3) Recognize polynomial
functions and rational functions from their
graphs (5.2, 5.3) Sketch a rough graph of a
polynomial or rational function using a grapher
to refine your picture (5.2, 5.3) Interpret
characteristics of polynomial or rational
functions in context (5.1,5.2, 5.3)