<p>Hey guys
wasn't sure if I should be posting in this section for help, but it did say preparation so I might as well..</p>
<p>My question came up on one of the practice tests I was taking. Goes as follows:
If f(x) = radical(x^2), then f(x) can also be expressed as...</p>
<p>I thought it was just x or at least +/- x, but it said the answer is lxl "l l" meaning absolute zero symbol.</p>
<p>Thank you!
p.s. i might just use this thread to continue posting any more sat math 2c problems i encounter rather than just opening up a billion threads :)</p>
<p>The answer would be lxl since it is x^2 under the radical. If it was asking for the cubed root of x, the answer would not be in absolute value form. Even exponents of x taken out from under the radical would be in absolute value, odd ones would not. For example:
the square root of (x^3) would simplify to lxl radical x
the cubed root of (x^3) would simplify to just be x</p>
<p>Feel free to post other questions here since aren’t any other sections dedicated to subject tests.</p>
<p>i see thank you triassiic for the explanation, but one more thing, are you saying any radical under an even root will form a lxl situation?</p>
<p>so like radical4(x^2) would be lxl but radical 4(x^3) would not?</p>
<p>and yeah i intend on doing that ndl1920 lol. im a rising senior and i need to finish my 2c by sept. -___-</p>
<p>:/</p>
<p>I think the confusion is stemming from the sqrt operation. The principal sqrt of a non-negative has only one value. For example, sqrt(1)=1 NOT +/- 1. To see why sqrt(x^2) is |x| consider two cases: x>=0 and x<0.
If x>=0 then sqrt(x^2)=x
If x<0 then -x>0 and sqrt(x^2)=sqrt((-x)^2) which is equal to -x by case 1.
So we have sqrt(x^2)=x if x>=0 and -x if x<0, which is the definition of absolute value.</p>
<p>It depends if you are talking about the square root or the cubed root. All even exponent values of “x” under the radical (SQUARE root), when simplified, will be in absolute value form</p>
<p>Not quite, you won’t always need absolute value signs with even indices. For example sqrt(x^4)=x^2. |x^2| is just redundant.</p>
<p>Correct. You only need it for square root of x^2</p>
<p>Or more generally, one does not need absolute value bars anytime the power of the radicand divided by the index is even.</p>
<p>If x >=0 then f(x) = sqrt(x^2) = x</p>
<p>If x < 0 then f(x) = sqrt((-x)^2) = x</p>
<p>Therefore f(x) = |x| for all x.</p>
<p>You have a typo in your second line. If x<0 then sqrt((-x)^2)=-x since -x>0. You have described the function f(x)=x, not f(x)=|x|</p>
<p>okay thanks guys:
another question came up today when something varies jointly what does it mean?</p>
<p>i think my school teachers taught it to us incorrectly because i get the wrong answer. the question goes:</p>
<p>if y varies jointly with x, w, and z^2 what is the effect on w when x, y, and z are doubled?</p>
<p>the answer is w is divided by 4</p>
<p>I believe jointly just means that y equals the product of x, w, and z^2. Therefore y=xwz^2, which becomes w=y/(xz^2). If you double x, y, and z, it becomes (2y)/(2x4z^2), which cancels to y/(4xz^2). Compared to the original, this has a 4 in the denominator, which equates to dividing w by 4.</p>
<p>Aqua’ solution is correct, but the definition of joint variation means that y is PROPORTIONAL to the product of x,w, and z^2. I mention this because a question might ask something like If y varies jointly with a,b, and c and y=30 when a=1,b=3,c=5, what is the value of bc when y=4 and a=2. In a case like this the constant of proportionality would not be 1.</p>
<p>thank you. also what does it mean to be a continuous function?</p>
<p>for one of the problems on my practice test i got a problem asking when would F be a contintuous function if </p>
<p>F(x) = {(3x^2)-3/(x-1), when x does =/= 1<br>
k, when x = 1}</p>
<p>What value(s) of K is F a continuous function?</p>
<p>First how would you even solve these types of problems? I always have difficulty with what the given information is trying to say</p>
<p>also how would you find the units digit of a certain number</p>
<p>the question asked what ht eunits digit of 1567^93?</p>
<p>If a function is continuous at a point, then the limit at the point equals the function’s value. The lim ->1 F(x)=lim x->1 (3x^2-3)/(x-1)=lim x->1 3(x-1)(x+1)/(x-1)=6.
The value of the function at x=1 is k, so k=6</p>
<p>To solve the second problem we look for a pattern in the units digits of powers of 7. We see that it has length 4, so we look for the remainder after dividing 93 by 4.</p>
<p>7^1=7 mod 10
7^2=9 mod 10
7^3=3 mod 10
7^4=1 mod 10
7^5=7 mod 10 and now it repeats. 93=1 mod 4 so the units digit is 7</p>
<p>thre’s a problem that asks if p/r is an integer, which of the following must also be an integer?</p>
<p>i have trouble with these types of problems; is there any other way by solving these problems rather than plugging in numbers (which is probably a bad way of solving these problems, but it’s the only way I know how to … LOL).</p>
<p>the answer choices are p-r, p+2r, r/p, pr, 2p/r</p>
<p>also how do you determine if a function is even or odd?</p>
<p>If p/r is an integer then 2p/r must be an integer since we can write it as 2(p/r). Integers are closed under multiplication, so this product of integers is also an integer.</p>
<p>f(x) is an odd function if f(-x)=-f(x)
f(x) is an even function if f(-x)=f(x)
Ex: f(x)=sin(x) is odd because sin(-x)=-sin(x)
f(x)=x^2 is even because (-x)^2=x^2
f(x)=e^x is neither odd nor even since e^(-x) is not equal to -e^x or e^x</p>