Practice Exam 3
1. Sketch the graph of the following functions. Be sure to include all intercepts and asymptotes. (horizontal, vertical, or slant) (a) p(x) = x3 - 2x2 - x + 2 (b) p(x) = x4 - 4x3 + 3x2 + 4x - 4 (c) p(x) = x5 - 4x3 - 2x2 + 3
m ONE-TO-ONE FUNCTIONS AND THEIR INVERSES
A B A B
f is one-to-one g is not one-to-one
DEFINITION OF A ONE-TO-ONE FUNCTION
A function with domain A is called a one-to-one function if no two elements
of A have the same image, that is,
ALGEBRA 0F FUNCTIONS
Let f and g be functions with domains A and B. Then the functions f + g,
f g, fg, and 3%; are dened as follows.
(f + 9X1) = f0?) + 9(X) DomajnA n B
(f 9090 = f(x) _ 9U) Domain/I n B
(f9)(I) = f(x)g(x) DomajnA n B
m LINEAR FUNCTIONS AND MODELS
A linear function is a function of the form f(x) = ax + b.
The graph of a linear function is a line with slope a and y-intercept b.
EXAMPLE 1 Identifying Linear Functions
Determine whether the given functio
m TRANSFORMATIONS OF FUNCTIONS
VERTICAL SHIFTS OF GRAPHS
Suppose c > 0.
To graph y = f(x) + c, shift the graph of y = f(x) upward c units.
To graph y = f(x) c, shift the graph of y = f(x) downward c units.
EXAMPLE 1 Vertical Shifts of Graphs
Use the gra
m AVERAGE RATE OF CHANGE OF A FUNCTION
.l Average Rate of Change
We are all familiar with the concept of speed: If you drive a distance of 120 miles in
2 hours, then your average speed, or rate of travel, is 12%, = 60 nii/h. Now suppose you
take a car tri
DEFINITION OF A FUNCTION
A function f is a rule that assigns to each element x in a set A exactly one
element, called x), in a set 3.
We usually consider functions for which the sets A and B are sets of real numbers.
The symbol x) is read f of x or f at
m GRAPHS 0F FUNCTIONS
THE GRAPH OF A FUNCTION
If f is a function with domain A, then the graph of f is the set of ordered pairs
cfw_(16, f(X)| x E A
plotted in a coordinate plane. In other words, the graph of f is the set of all
points (x, y) such that y
TEST #3: CHAPTERS 6
ORGANIZATION OF TEST
(Note: test has not been finalized yet, so this is subject to changes)
Part I: Numeric Answers: (25 questions @ 1)
Part II: Explain questions: 12 points (3 @ 3)
Total (will count for 100 percentage
Math 141 Monarres
Practice Exam 1 February 13, 2007
1. Find all real numbers x that satisfy the following inequalities. Express the solution in interval notation. (a) -14x + 3 -5 (b) 15x + 2 < 2 (c) x2 - 5x - 6 0 x-4 (d) x-2 3 x+5 (e) 16x2 25 (f)
Math 141 Monarres
1. For the following functions, f (x) and g(x), find (f + g)(x), (f g)(x), domain of each new function. (a) f (x) = (b) f (x) = (c) f (x) = x (d) f (x) = x2 - 2 2. Consider the functions 1 g(x) = x - 2 h(x) = x2 - 7 x+2 (a) Find (
MATH 141 Final
12/8/06 10:22 PM
MATH 141 Final SPRING 2006 Version A
Name: _ Instructor: _ Section Time: _
1. Which of the following functions is best described by the graph below
Math 141 Precalculus Final Exam Version A Answers 1. 2. 3. 4. 5. 6. 7. B D A D A A D
8. A 9. B 10. E 11. D 12. E 13. B 14. C 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. C C C C A A D D A B C E E C C D D D