<p>For the question regarding the function f(x-1), it was definitely a shift to the right, correct?</p>
<p>Yes. This is the same way as a parabola x^2 shifted one unit to the right becomes (x-1)^2.</p>
<p>*Repost on this page… edited to include noseferatu’s addition</p>
<p>Entire thread:</p>
<p>** 1.85 for sqrt(2+sqrt(2)), 1st question
** 2.2 for (a^3)^2 equals 123.1
** 30% for the profit on the jeans
** 29.69 for the perimeter of the triangle (or 3<em>7sqrt(2))
*</em> 2sin(theta) for the unit circle thing, length of chord AB
** .997 for fire alarm probability
** 39.55 for bouncing ball (anyone remember how many bounces it was?)
** “x=y or t=0” for under what conditions would xt=yt be true
** -x^2 + 2
** 1+a^2 for the tan(?)=sec^2(a) or whatever
** SHIFT TO THE RIGHT for g(x)=f(x-1)
** ALL THREE SIDES needed for finding the angle B
** 8 factors for where 3 prime factors are equal and 1 is different
** 5 is the first in the arithmetic sequence
** 5 judges needed to get 5.4 as a mean
** x>3 for |x-3|/(x-3)=1
** s<em>sqrt(3)/2 for the radius of the sphere with the inscribed cube
*</em> t>=3x for the logic problem where it said t<3x if 1<y<4, which it wasnt
** 6! for the permutations of 8 colors with 2 of them being set
** NONE for integral numbers on the line between (0,0) and (73,83)
** 7.78% increase for NYC after 25 years, with the .3% annual increase
** -.83, or -3/sqrt(13) for where its the sin(theta) where the point is (-2,-3)
** .93 for the length of the minor arc
** PI/2 for cos(x-k)=sin(x)
** Only I and II for temperature of cheese (starts at 75, approaches 55, but does NOT reach 50)
** Only I and II for which of the functions can fit the graph (-sin(x),|sin(x)|, but NOT cos(x))
** 2.6 for the greatest zero of the equation x^4-2x^3-8x^3+14x+7
** 2 3 or 4 for the # of distinct roots – “are different for at least one value of x” was basically the wording
** (2,-4,0) was the point double the distance from the origin to (-1,2,0) the other way
** 0<x<3 for what x values give a greater y value for the line than for the parabola
** (x-1)^2 + (y+2)^2 = 4 for which equation puts (1,2) outside the circle
** -1 for (2x-1)^2 + (2y+3)^2 = 0 and it asks for x + y
** 4.8 (E) for cone problem</p>
<p>^^^^^^^^33 so far
here’s another question that was mentioned in the thread but was never given an answer, I think.
tan(x) = something and tan(y) = something else, what is whatever?</p>
<p>Any clarifications of, challenges to, or additions to the list?</p>
<p>Will a 43 right 4 wrong and 3 omit be a 790? or 780?</p>
<p>If the curve is the standard 43, then that’s a 790.</p>
<p>I can’t comment on what the curve would be, because I’ve never taken this test before yesterday. Practice tests wouldn’t be a proper thing to compare it to.</p>
<p>I’m not sure about that shift question I thought it was a shift to the left, but maybe I screwed up. There was a question about if this graph is f(x) which graph is |f(x)|. The answer was pretty obvious, but I can’t remember the letter. I’m only shooting for a 700ish score (I’m not shooting for engineering or anything) so I’ve got like 4 wrong so far and left 7 blank, so I’m not too worried yet.</p>
<p>I seem to recall the answer to the first question as being two, although I can’t remember what the question was.</p>
<p>Gkilla: That’s a 780-800 range, approximately.</p>
<p>DmctNY8: here’s my proof from earlier in the thread:</p>
<p>Consider f(x) versus f(x-1):</p>
<p>f(x):
f(0) = 0; thus (0,0)
f(1) = 1; thus (1,1)
f(2) = 2; thus (2,2)
f(3) = 3; thus (3,3)</p>
<p>f(x-1):
f(1) = 0; thus (1,0)
f(2) = 1; thus (2,1)
f(3) = 2; thus (3,2)
f(4) = 3; thus (4,3)</p>
<p>If you notice, in the second equation the x value is increased by one at each specific y value. Thus the graph shifts rightward one unit.</p>
<p>seriously, i think the answer to the polynomial is 3 or 4 distinct roots. This is because they need to have 1 point that is different so the 2 poly nomials can’t be the same equation with the same roots.
(x-3)(x-1) cannot times (x-3)(x-1) because they are the same.
Anyway plz tell me why i’m wrong.</p>
<p>Yes, but was that what the question was, I agree that that would be right if the question asked for that.</p>
<p>These two equations have two distint roots but aren’t the same: m(x-a)(x-b) and n(x-a)(x-b) notice m does-not-equal n.</p>
<p>I got that one wrong too.</p>
<p>They asked: if this is the graph of f(x) [graph shown], what would the graph of f(x-1) look like.</p>
<p>H20Poloer: Here’re two versions of the proof for the polynomial question:</p>
<p>Abstract Proof:</p>
<p>h(x) can have 2 roots if f(x)=m(x-a)(x-b) and g(x)=n(x-a)(x-b); h(x)=mn(x-a)^2(x-b)^2 and you have two distinct roots.</p>
<p>h(x) can have 3 roots if f(x)=m(x-a)(x-b) and g(x)=n(x-a)(x-c); h(x)=mn(x-a)^2(x-b)(x-c)</p>
<p>h(x) can have 4 roots if f(x)=m(x-a)(x-b) and g(x)=n(x-c)(x-d); h(x)=mn(x-a)(x-b)(x-c)(x-d)</p>
<p>Concrete Proof:</p>
<p>h(x) with 2 roots:
f(x) = 2(x-1)(x+2) ; g(x) = 3(x-1)(x+2)
f(3) = 2(2)(5) = 20 ; g(3) = 3(2)(5) = 30
h(x) = 6<em>(x-1)^2</em>(x+2)^2 ; two zeros: 1 and -2</p>
<p>h(x) with 3 roots:
f(x) = 2(x-1)(x+2) ; g(x) = 3(x-1)(x+3)
f(3) = 2(2)(5) = 20 ; g(3) = 3(2)(6) = 36
h(x) = 6<em>(x-1)^2</em>(x+2)(x+3) ; three zeros: 1, -2, -3</p>
<p>h(x) with 4 roots:
f(x) = 2(x-1)(x+2) ; g(x) = 3(x-4)(x+3)
f(3) = 2(2)(5) = 20 ; g(3) = 3(-1)(6) = -18
h(x) = 6(x-1)(x+2)(x+3)(x-4) ; four zeros: 4, 1, -2, -3</p>
<p>General Rak is probably tired of explaining that, so… if you have coefficients, then there will be points that are different. Consider m(x-3)(x-1) != n(x-3)(x-1)</p>
<p>And DmctNY8, the question asked for f(x-1) if the thing shown at the top was f(x)</p>
<p>And I too kind of recall the first question’s answer being 2, though I remember the question itself almost certainly to be sqrt(2 + sqrt(2))… which is 1.85. Did that possibly round to 2?</p>
<p>I hate how these tests are designed to be tricky, it’s so frusturating because I know how transformations work I just misread the stupid question.</p>
<p>GOD DAMMIT
who makes these tests?</p>
<p>For some reason the equations you guys have come up with for the first question seem ever so slightly different than the actual one.</p>
<p>i forget the question, but does anyone remember putting down 49 as an answer?</p>
<p>i thought the graph question was
“If the graph shown is f(x-1) what is the graph of f(x)”
so my answer was the graph that was shifted one unit to the left.
am a right or did i read the quesiton wrong?</p>
<p>You read the question wrong.</p>
<p>damn it!
hopefully that was the only question i got wrong besides that x<3t then 2<y<6 or w/e the problem was. I put x greater than or equal to 3t. i dunno if thats right.</p>