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Unformatted text preview: October 29, 2004 HA'l'II I I 3  'I'ES'I' 2 NAME:
A
SECTION:
QA4D
Instructions: Do all problems in the spaces provided. Mark your answers clearly and write them in simpliﬁed form. You must show all
appropriate work in order to receive credit for an answer. You may NOT use calculators of any type on this exam. Find g 1. (a) f(x)=5"‘2, g(x)=5" [5]
1o 1
(b) Evaluate: lne + 10g4 E + 10g4 1
[6]
(0) Does the function y = 6” represent and increasing function or a decreasing function ?
[4]
x2 — 4 x — 4 x
9. f (x) = g(x) = 2 1106) = ' 2
x x x — 4
[9]
For each of the following statements, name all of the above functions (f g, and/or h) for which the statement is true:
(i) The line x = 2 is a vertical asymptote of the graph of the function.
(ii) The line y = 0 is a horizontal asymptote of the graph of the function.
(iii) The domain is all real numbers except 0. A page 1 of 4 3. A ﬁlmiture manufacturer has a daily production cost given by the model C = 1200 — 200x + 10x2 where C is the
total cost in dollars and x is the number of units produced.
(a) How many units should be produced each day to yield a minimum cost ?
[6]
(b) Explain how you would determine the minimum cost.
[3]
4. (a) If a function is an EVEN function, explain what you know about its graph .
[4]
(b) Graph a function, f, such that f (0) = —2, f (—4) = 3 and the function f does not have an inverse.
[6] 
(c) On what interval(s) is the function f, whose graph is below, increasing ?
[4]
5. Sketch the graphs of each of the following on the axes provided. Label at least one point on each graph with its
coordinates, and label any asymptotes with their equations.
(a) f(x) = —ix — 1‘ — 3 (c) h(x) = e"—3
[6] [6]
f(x) W)
+ X X
A page 2 of 4 .______—._..——_.___.________.___.__.._________________________. ___ __ _ _ 6. (a) The perimeter of a rectangular ﬁeld is 640 ft., where w represents the width of the ﬁeld and 1 represents the length.
Write a quadratic function that expresses the area of the ﬁeld in terms of its width, w. [6] (b) Given the quadratic function g(x) = —7(x — 5)2 1 , complete the following: The vertex of the function g is the point , and the function has a value of
[6] (maximum/minimum) x—4
x+2 7 f (x) = (a) Find the x and y intercepts, showing your work algebraically. [4] (b) State the equations of the vertical and horizontal asymptotes. [4] (c) Sketch the graph of f, plotting the x and yintercepts drawing the asymptotes. [5] A page 3 of 4 8. [6] 9. [6] [4] Verify, using composition of functions, that the following functions are inverses of each other: f(x) =3x/6—x g(x) = 6x3 (a) Determine the zeros of the function f (x) = x4 — 36x2 . State the multiplicity of each zero. (b) Discuss the right and lefthand behavior of the graph of f. Copy the following pledge and sign your name:
I pledge on my honor that I have not given or received any unauthorized assistance on this examination. page 4 of 4 ...
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 Spring '08
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 Algebra

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