TMAT 155
Topics for Final Exam, Spring 2009
Chapter 1: Functions, function notation, difference quotient, graphs of functions, domain,
range, maximum, minimum, x- and y-intercepts, composition of functions (f º g and g º f),
reversing composition, inverse functions, one-to-one, graphing corresponding points of
inverse functions
Text Secs 1.2, 1.3, 1.5, 1.6
Chapter 2: Parabolas including all intercepts, vertex, axis of symmetry; long division and
synthetic division; complex numbers (all operations including rationalizing denominator), roots
of higher degree equations, finding the factors irreducible over the reals (uses synthetic
division), multiplicity, factor theorem, finding a complete factorization of a polynomial using all
roots
Secs 2.1, 2.3, 2.4, 2.5
Chapter 3: Compound interest and continuous compounding (A = Pe rt), graphs of exponential
and logarithmic functions (know x- and y-intercepts, asymptote, domain, range), exponential
form of a log equation, finding values of logs by hand and by change-of-base, all laws of
logarithms, expansion and contraction, solving logarithmic and exponential equations by
hand, applications to problems involving continuous growth or decay, doubling time, half-life
Secs 3.1-3.5
Chapter 4: Radian and degree measure, arc length, the six trig functions, solving right
triangles, word problems involving right triangles (finding a side or an angle), angles of
elevation and depression, special angles (multiples of 45 º, 30 º, or 60 º), sketch reference
triangle with all detail, finding the other 5 functions given one function and given the
quadrant, finding the angle given a trig function value and given the quadrant, graphs of sine
and cosine functions (give a detailed sketch of 1 cycle, know amplitude, period and phase
shift), graphs of tangent and secant functions (know domain, range, asymptotes, x-intercepts),
inverse trig notation (see reminder below)
Secs. 4.1, 4.3-4.6
Chapter 5: The eight fundamental identities (five basic and three Pythagorean), simplifying
trig expressions using these identities, proving other trig identities by simplifying each side
separately, sums and differences (sine and cosine only), double angle, half angle
Secs. 5.1, 5.2, 5.4, 5.5
Chapter 7 (Sec. 7.2 only): Solve a system of two linear equations in two unknowns
algebraically and check your answers
Reminder: arcsin x = sin-1x, arcos x = cos-1x, etc.