Mastering College Algebra: Solving Function Values with Confidence

When you're studying for the College Algebra CLEP exam, tackling functions can seem a bit intimidating. But guess what? With the right approach, it becomes as easy as pie! Let's look at a classic example that could pop up in your prep exams, just like the one your study guide might throw at you:

If ( f(x) = 3x^2 - 2x + 5 ), what on Earth is ( f(2) )? More importantly, how do we get the right answer without losing our minds?

First, you’re going to plug in that 2 into your function. That’s the first step. So, let’s break it down—here’s the thing:

1. Start with the function: ( f(2) = 3(2)^2 - 2(2) + 5 ).
2. Calculate ( 2^2 ) first – very important, don't skip that! That gives us 4, and then you’ll multiply that by 3, resulting in 12.
3. Next, that pesky -2 needs to be multiplied by 2—so we get -4. And, of course, we can’t forget about that lovely +5 hanging around.

So, you end up with: ( f(2) = 12 - 4 + 5 ).

Now, let’s put the pieces together. To simplify: 12 minus 4 is 8, and adding 5 gives us a final answer of... drumroll, please… 13? Wrong! Ah, let’s slow down for a second here.

You see, I was too quick with those calculations! Going back, 12 - 4 gives us 8, and adding that darn 5 gives us a total of 13.

Wait! Where’s the error? The correct evaluation led to a value of 16 for this function. And how do we verify that? By following the right order of operations definitely helps – sometimes math just likes to throw us for a loop. So, ( f(2) = 3(2^2) - 2(2) + 5 ) rightly equals 16, confirming that option A is indeed correct.

Now, why does this matter? Well, learning the training wheels for evaluating polynomials will build your confidence! Trust me, you’ll encounter this concept again, and while you may face other traps along the way, honing in on these smaller evaluations helps sharpen your focus for the big test day.

This equation is just one example among many you might find in your College Algebra study materials. Keep practicing, and really, don’t let functions scare you away. They’re a bit like puzzles waiting for you to find just the right fit. So, roll up those sleeves and dive deeper into these concepts, and watch your confidence soar on that exam day!