Allow me to preface this by introducing myself and explaining a little about my background and where I'm going with this.
My name is Shawn, I'm from Las Vegas and I'm three credit hours from completing my Paralegal Degree and certificate program. I'm 33 years old and I when I originally took my math placement test for school in 2007, I placed very low because I hadn't used any kind of advanced math since 1992. I have never had a problem learning math.
A Math class of 120 (Fundamentals of College Mathematics) or above is required for my degree. Because of my low placement scores, I was required to take Math 096 (Intermediate Math) as a pre-requisite for 120 or 124 (College Algebra).
I put the math on the back burner and I completed the entire remainder of the Paralegal Program in December 2008. My plan was to simply study, get a tutor, self-teach and CLEP out of either 120 or 124. When I contacted the private tutoring service, they suggested that I focus on College Algebra. The problem that I ran into is that I simply didn't have enough time to learn the entire course to take the CLEP. Even though I understood what I learned, there was far too much information to absorb for the 10 hours I had paid for at $500. Looking back I realized I should have focused on the 120 instead and tried to CLEP out of that class which I could have done a lot easier as it's not nearly as Algebra intensive and a third of it has to do with what I learned in Critical Thinking which I got an A- in (truth tables, Venn diagrams, etc.).
Regardless, between the amount of independent studying I did and the amount of tutoring I received, I took the placement test last week and was one correct answer away from qualifying for either 120 or 124. Now, I can't take the placement test for four months.
But, there is another solution: I can take a "diagnostic test" that covers the materials of 096 (Intermediate Algebra) to qualify for 120. This means the difference between six weeks in a summer class where all I have to do is basically survive it and get a C (3.94 GPA so that's not likely) or six months (a six week summer session and a 16 week fall session) taking two classes. The urgency is because of my job (and my wife who is going to punch me in the head). My law fim cannot bill me out as a Paralegal until I have my degree and certification. It's not a rule or a law, it's simply what their clients (corporations) require. Also, the quicker I get this done the quicker I get promoted and get paid a heckuvalot more than what I'm making now.
The college is very good on providing links to online materials to show students exactly what they need to learn. The only reason I'm posting this in Pre-Calc is because that's the title to the first link it directed me to here.
I've gotten 3/4 of the way down the page and I'm working on the concepts of functional notation. I'm having trouble with one problem in particular because the answer doesn't make sense to me.
Problem 6. Let f(x) = 4x². Write what results when f operates on eachAnd here's what it shows for the answer:d) f(x − 5)
Now I got as far as 4(x − 5)² but my FOIL from that point came up with a completely different answer.4(x − 5)² = 4x² −40x + 100
What am I missing? Here's my logic:
When you have (x − 5)² with a minus sign in the middle, do you not break it down to look like this: (x - 5) (x + 5) and then do your FOIL accordingly?
F = x²
O = 5x
I = -5x
L = -25
So you have 4(x² + (5x - 5x) -25) or 4x² - 100.
The answer provide makes sense only if this f(x − 5) was this f(x + 5)
Am I completely off-base here and am I scewing up my concepts.
I have to get these concepts down quickly so any help that can be provided would be greatly appreciated. Please be gentle iwth me and keep in mind that I'm not a math major but I can figure out math concepts if explained to me.
Thanks in advance.
-Shawn
This is true, but are we multiplying a negative number by itself, like -5 times -5? No, we are multiplying a polynomial (more accurately, a binomial) by itself, and as such, you don't change the sign inside. So
(x - 5)² = (x - 5)(x - 5).
If you had something like (-5x)² , however, you would get
(-5x)² = (-5x)(-5x) = 25x²,
which does give you a positive coefficient.
01
Is this what you're looking for?
Assuming that's a yes, let's plug that into the function:
There's a rule where if you have two numbers multiplied together that is being raised to an exponent, then you can raise each factor to that exponent:
Now 1/2 squared is 1/4:
If you take a square root of a number, and then square the answer, you are left with the original number. So you can "cancel out" the square root and the exponent of 2:
4 times 1/4 is 1:
or
01