<ol>
<li>Suppose the graph of y =f(x) has a vertical asymptote at x = 4 and a horizontal asymptote at y = 1. If g(x) = 1/2 [f(x)], which lines are the asymptotes of the graph of g(x)?
(A)x=2, y= -1/2
(B) x=2, y= -1
(C) x=4, y= -1
(D) x=4, y= -1/2
(E) Not enough information to tell </li>
</ol>
<p>the answer is D</p>
<p>The answer is D because 1/2 f(x) basically means scaling the y-axis of f(x) by 1/2. The x-axis is NOT affected.</p>
<p>thanks maggypro!</p>
<p>i’ve got another question
In an arithmetic sequence a(subscript)n, a(subscript)7= a(subscript)3 + 18 = 4
which of the following equation is true ? ()=subscript
(A) a()n = -5 + 4n
(B) a()n = -27.5 + 4n
(C) a()n = -5 + 4.5n
(D) a()n = -27.5 + 4.5n
(E) a()n= -27.5 + 6n</p>
<p>the answer is (D)</p>
<p>We have a<em>7 - a</em>3 = 18, so the common difference is 18/4 = 4.5, so this removes A, B, and E.</p>
<p>Only answer choice D satisfies a_7 = 4 (just plug in n = 7).</p>
<p>and yet another question.
f(x) =3 sin 3x and the domain of f(x) is b =< x =< b .If the graph of f crosses the x-axis exactly 7 times, which of the following could be b? </p>
<p>(A) pi/6
(B) pi/3
(C) 5pi/4
(D) 3pi/2
(E) 2pi</p>
<p>ans is (c)</p>
<p>thanks!</p>
<p>Basically, the strategy with dealing with hard questions is not to get intimidated by them. Try reading it slower, and break up the problem.</p>
<p>First, graph f(x) = 3 sin 3x. It will cross the x-axis at x = 0, ±pi/3, ±2pi/3, ±pi, ±4pi/3, etc. (all multiples of pi/3). </p>
<p>We want exactly seven crossings of the x-axis in [-b, b] so suppose f(x) crosses the x-axis at 0, ±pi/3, ±2pi/3, and ±pi. Setting any value of b in the interval [pi, 4pi/3) will do the trick. Answer choice (C) works, since 5pi/4 is between pi and 4pi/3.</p>
<p>thanks for helping!
however, i don’t exactly get why the value of b shouldn’t just range from -pi to +pi (that is, b = pi) why should it lie between pi and 4pi/3</p>
<p>pi also works. b must be in the interval [pi, 4pi/3).</p>
<p>i finally get it. yay!!</p>