Understanding Functions: A Simple Breakdown of g(x) = 4x - 1

Understanding Functions: A Simple Breakdown of g(x) = 4x - 1

Getting ready for the Ontario Mathematics Proficiency Test? One of the skills you’ll need is figuring out how to evaluate functions. Let’s break down a simple example together—how do you find g(3) if the function is defined as g(x) = 4x - 1?

It’s All About Substitution

First off, functions may seem intimidating, but they work like a recipe in cooking—substituting ingredients to get your desired dish! So, for g(x) = 4x - 1, you’re simply going to substitute the value of x with 3. Let’s lay out our steps:

1. Substitution:
   Start with g(3) = 4(3) - 1
2. Calculate:
   Okay, time for the math magic! Multiply 4 by 3, and what do you get? That’s right, 12!
   So now we have g(3) = 12 - 1
3. Final Step:
   Let’s just subtract 1 from 12. And there you go, g(3) = 11.

Boom! We’ve just evaluated the function, and the correct answer is indeed 11! But why does this matter? Understanding how to work with functions like this one not only boosts your math skills but also strengthens your problem-solving approach.

The Other Options: What Went Wrong?

Now, you might be wondering about the other options provided: 10, 12, and 13. They’re all different paths you could have taken, but only one leads you to the right answer.

• 10 would imply you mistakenly calculated as if you added 1 after multiplication.
• 12 could be someone who forgot to subtract altogether.
• 13 might come from a weird addition error.

Each of these options represents potential miscalculations, showing the importance of following the right steps. And trust me, it’s common to make little mistakes like these!

Putting It All Together

So, the moral of the story? Don’t sweat the small stuff. When working with functions, take a step back and remember the process: substitute, calculate, and simplify.

Understanding how to evaluate g(x)=4x-1 sets you up for success in the Ontario Mathematics Proficiency Test and beyond. Keep practicing and remember, each function can help build your math muscle—so embrace the challenge!

Wrapping It Up

In conclusion, mastering these concepts now pays off down the road. So the next time you're faced with a question about functions, just take a deep breath and follow the steps. Remember, you have what it takes to get the answers you need. Happy studying!