Math 151      Study Guide for Hour Quiz #1       C.S.Davis

You are responsible for the subject matter in the sections below. The following topics are the most important. Typical exercises from Precalculus, 5th edition, by Stewart, Redlin & Watson are assigned at the end of each objective. Work additional exercises if you need more practice. The answers to the odd numbered problems are in the back of the text.  These exercises are for practice and are not graded.  The problem sets found on the PreCalculus Welcome Page are graded in class.  See the Semester Plan for the current dates for the grading of the problem sets and taking of the hour quizzes.
2.1          Applications in calculus require verbal descriptions and explanations.
1. Given a function in algebraic form, 
a.  describe it verbally;   P155#5
b.  illustrate it with a machine diagram and an arrow diagram;   P155#9
c.  evaluate it at numerical values and at symbolic values;   P155#17,21,29,31
d.  find its domain.   P156#43-51odd,57
2.2         Analysis of graphs is important in calculus when a formula is not available.
1. Given a graph of a relation,
a.  determine whether it is the graph of a function using the vertical line test;   P167#55
b.  if it's the graph of a function, evaluate the function at numerical values and find the domain and range.   P167#23,24,57
2. Given the rule (algebraic form) of a function,
a.  form the t-table and sketch the graph by hand and find the domain.   P167#7,19,27
b.  use a grapher to graph the function and transfer the graph and window to paper.   P167#33,35,53
3. Given the rule for piecewise functions, do (a) and (b) in item (2) just above.   P167#39,45,49,51
2.3         Average rate of change is used in calculus to define instantaneous rate of change.
1. Using algebra, graphs and tables, find average rate of change and intervals where the function is increasing or decreasing.   P179#1,9,13,15,19,21,31,33,35
2.4         Transformations on functions allows us to create many functions used in calculus from just a few.
1. Perform the transformations of reflection, stretching, and translation (shifting) on equations, functions and graphs of equations and functions.   P199#1-45odd,73
2. Determine whether a given function is even, odd or neither.  If even or odd, use the right half of the graph to sketch the left half.   P192#55,61,63,65,69
2.5          Next to straight lines, quadratic functions are used most often in calculus 
1. For the equation of a given parabola, complete the square to find the vertex , factor (or use quadratic formula) to find the x-intercepts, and sketch the graph by hand.   P201#15,23,59,61,65
2.6          Mathematical modeling is the reason calculus is required in so many disciplines.
1. Solve a word problem that involves extreme values (max/min) of a quadratic function.   P211#23,24
2.7          Function composition is a general way to create many functions used in calculus from just a few.
1. Perform arithmetic on functions. (add, subtract, multiply and divide functions.   P219#5
2. Add, subtract, multiply and divide functions graphically.   P220#11,13
3. Perform composition of functions algebraically and find the domain of the composite function.   P220#17,19,21,29,37,57,61
4. Perform composition of functions graphically.  P220#23,25,27
5. Decompose a composite function into its component parts.   P220#45,47
2.8          Inverse functions have special properties in calculus.
1. Determine whether a function is one-to-one.   P230#1,3,5,9,13,55
2. Determine whether two given functions are inverses of each other by showing f(g(x))=x and g(f(x))=x.   P230#23
3. find the inverse function for a given one-to-one function.   P230#33,39,41