Understanding the Function F(x) = x(-x) and Finding F(3)

Let’s unravel a classic algebra problem that often trips up students during tests: evaluating the function ( F(x) = x(-x) ) at ( x = 3 ). It’s all about substitution and simplification, so grab a pencil and let’s dive in—you won’t want to miss this!

So, here’s the function we’re working with: [ F(x) = x(-x) ] At first glance, it might look a bit confusing, right? But don't worry; I promise it's straightforward once you break it down. Think of it like you’re just following a recipe—one step at a time.

To find ( F(3) ), we replace ( x ) in the function with 3. This is the fun part—let’s do it together! When you plug in 3, it transforms into: [ F(3) = 3(-3) ]

Now, you might be wondering, what do I do with those numbers? Well, since we’re multiplying, it’s like saying you have 3 times the negative of 3, which sounds rather intense, doesn’t it? Here’s the math: [ F(3) = 3 \times (-3) ] Carving that out gives us: [ F(3) = -9 ]

Aha! There you have it—the answer is -9! It’s fascinating how just a little multiplication led us here, and it really emphasizes the power of understanding negative numbers. Now, why does this matter? This is the kind of fundamental concept that you’re likely to encounter not just in algebra tests, but also in real-world scenarios, like calculating losses in a business, or even distributing negative quantities in various fields.

Plus, think about it: when you multiply a positive number by a negative number, the result is always negative. It’s a solid rule that holds true, no matter what—kind of like the golden rule of algebra, if you will!

By understanding how to manipulate functions like ( F(x) = x(-x) ), you’re not just preparing for a test—you’re building a foundation for higher-level mathematics. Remember, the more practice you get under your belt with these functions, the easier they become. Who knows, maybe someday you’ll be teaching someone else this same concept!

So as you take on more problems, keep this method in mind. Substitute, simplify, and take it one step at a time—it’ll pay off in spades when you face those algebra assessments. Keep calm, trust your process, and remember: you’ve got this!