Discover the Range of Relation 12x + 6y = 24 with the Given Domain {-4, 0, 5} - An SEO Title

Given The Domain {-4, 0, 5}, What Is The Range For The Relation 12x + 6y = 24?

The range for the relation 12x + 6y = 24 is {-8, 0, 2} given the domain {-4, 0, 5}.

Hold on to your hats, folks, because we're about to tackle a math problem that'll make your head spin! But fear not, dear readers, for I am here to guide you through it with a touch of humor and a lot of patience. So, without further ado, let's dive into the question at hand: Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?

First things first, let's break down what this question is even asking. The domain, in math terms, refers to the set of all possible x-values of a function or relation. In this case, we know that our domain consists of three values: -4, 0, and 5. Easy enough, right? Now, the range is the set of all possible y-values that correspond to those x-values. So, essentially, we need to figure out what values of y satisfy the equation 12x + 6y = 24.

Now, I know what you're thinking: Great, another algebra problem. Just what I needed to brighten up my day. But fear not, my friends, for I have a secret weapon up my sleeve: transition words! These little guys can make even the most mundane of topics sound exciting and engaging. So, let's sprinkle a few throughout this article and see if we can't make this math problem a bit more bearable, shall we?

Okay, back to the task at hand. We know that our equation is 12x + 6y = 24. But how do we solve for y? Well, we could use some good old-fashioned algebra and rearrange the equation to solve for y in terms of x. But where's the fun in that? Instead, let's use some deductive reasoning. If we divide both sides of the equation by 6, we get 2x + y = 4. Now, if we subtract 2x from both sides, we're left with y = 4 - 2x. Ta-da! We've solved for y without even breaking a sweat.

But wait, there's more! We still need to figure out what values of y correspond to our domain of {-4, 0, 5}. Let's start with -4. If we plug -4 in for x in our equation y = 4 - 2x, we get y = 4 - 2(-4), which simplifies to y = 12. So, when x is -4, y is 12. Easy enough. Now let's try 0. Plugging 0 in for x gives us y = 4 - 2(0), which simplifies to y = 4. So, when x is 0, y is 4. Lastly, let's try 5. Plugging 5 in for x gives us y = 4 - 2(5), which simplifies to y = -6. So, when x is 5, y is -6.

Now we have our three values of y: 12, 4, and -6. But is that all there is to it? Of course not! We need to make sure that these values are the only possible values of y for our equation. To do this, we can graph our equation and see if it passes through any other points. But let's be real, who has time for graphing? Instead, let's use some more deductive reasoning. If we look at our equation y = 4 - 2x, we can see that the coefficient of x is -2. This means that as x increases by 1, y will decrease by 2. So, if we start with our value of y = 12 when x is -4, and we increase x by 1 to get x = -3, y will decrease by 2 to give us y = 10. If we continue this pattern of increasing x by 1, we get the values of y = 8, 6, 4, 2, 0, -2, -4, -6, and so on.

So, what does this tell us? Well, it tells us that our three values of y (12, 4, and -6) are indeed the only possible values of y for our equation. Therefore, the range for the relation 12x + 6y = 24, given the domain {-4, 0, 5}, is {12, 4, -6}. And just like that, we've solved our math problem with a touch of humor and a lot of deductive reasoning.

But before we end this article, let's take a moment to appreciate the beauty of math. Yes, I said it: the beauty of math. Despite its reputation as a dry and boring subject, math has a certain elegance and simplicity to it that can be truly awe-inspiring. From the elegant simplicity of the Pythagorean theorem to the mind-bending complexity of calculus, there's something truly magical about the world of math. So, next time you're faced with a daunting math problem, remember to approach it with a sense of wonder and curiosity. Who knows, you might just find yourself falling in love with math all over again.

Introduction

Let's talk about range and domain - the two most important elements in mathematics. They are the bread and butter of any mathematical equation or function. Today, we'll be discussing the given domain {-4, 0, 5} and what the range is for the relation 12x + 6y = 24.

Domain and Range Explained

Before we dive into the specifics, let's first understand what domain and range are. Simply put, the domain is the set of all possible input values for a function or equation. On the other hand, the range is the set of all possible output values that result from those input values.

What is the Given Domain?

The given domain in this case is {-4, 0, 5}. This means that the only possible input values for our equation are -4, 0, and 5.

What is the Equation?

The equation we're working with is 12x + 6y = 24. This equation is in the standard form of a linear equation, which means that it's written in the form Ax + By = C, where A, B, and C are constants.

Finding the Range

Now, let's move on to finding the range for this equation. To do this, we need to solve for y:

Step 1:

First, we need to isolate y on one side of the equation by subtracting 12x from both sides:

12x + 6y = 24

6y = -12x + 24

Step 2:

Next, we'll divide both sides by 6 to isolate y:

y = -2x + 4

The Range

Now that we've solved for y, we know that the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope is -2 and the y-intercept is 4.

So, what does this mean for the range? Well, since the slope is negative, we know that the graph of the equation is a downward-sloping line. Additionally, since the y-intercept is 4, we know that the line intersects the y-axis at the point (0, 4).

Therefore, the range for this equation is all real numbers except for the values that would make y greater than or equal to 5 or less than or equal to -4. In other words, the range is:

{y | y ∈ ℝ, -4 < y < 5}

Final Thoughts

There you have it - the range for the relation 12x + 6y = 24 when the domain is {-4, 0, 5}. Remember, domain and range are essential elements in mathematics, and understanding them is crucial for solving equations and functions. So, keep practicing and have fun with math!

The Maths Question That Will Leave You Scratching Your Head

Are you ready for a challenge? It's time to solve the mystery of the (-4,0,5) Mafia and uncover the range of the ultimate equation showdown: 12x + 6y = 24. What do -4, 0, and 5 have in common? They're all part of this wacky relation that's sure to leave you astounded.

Solving the Mystery of the (-4,0,5) Mafia

As you embark on your journey to crack the code and unleash the power of 12x + 6y = 24, you'll need to understand the domain of the equation. In this case, the domain is {-4, 0, 5}. But what about the range?

The Range of 12x + 6y = 24: A Thrilling Tale of Math and Mystery

If you think this maths question is easy, we've got a bridge to sell you. The range of 12x + 6y = 24 is more exciting than a rollercoaster. From -4 to 5, there's a world of possibilities waiting for you.

But how do you find the range? It's all about solving for y. Let's start by rearranging the equation:

6y = -12x + 24

y = -2x + 4

Now that we have the equation in terms of y, we can plug in each value from the domain and solve for the corresponding y-value:

When x = -4, y = -2(-4) + 4 = 12

When x = 0, y = -2(0) + 4 = 4

When x = 5, y = -2(5) + 4 = -6

Why Did The Chicken Cross The (-4, 0, 5) Relation? To Find Its Range, Of Course!

Now that we have our three corresponding x and y values, we can determine the range of the equation. In this case, the range is {12, 4, -6}. That's right, the answer was staring us in the face the whole time.

So, why did the chicken cross the (-4, 0, 5) relation? To find its range, of course! And now that you've cracked the code and solved the mystery of the (-4,0,5) Mafia, you're ready for any maths question that comes your way.

The Hilarious Tale of the Domain and Range

Given The Domain {-4, 0, 5}, What Is The Range For The Relation 12x + 6y = 24?

Once upon a time, in a land far, far away (also known as Math class), there was a problem that needed to be solved. The teacher asked the students, Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?

The students furrowed their brows and scratched their heads. They had no idea what the teacher was talking about. But, there was one student who was different. His name was Jack, and he had a sense of humor that could make even the grumpiest teacher smile.

Jack's Point of View

Oh boy, another math problem. This is going to be fun! Jack thought to himself. He looked at the board and saw the equation 12x + 6y = 24. Easy peasy lemon squeezy, he whispered to himself.

Jack knew that the domain was just a fancy word for the x-values, so he wrote them down: -4, 0, and 5. Then, he plugged each of those values into the equation to find the corresponding y-values.

X-Value	Y-Value
-4	8
0	4
5	-1

Ah-ha! I've got it! Jack exclaimed. The range for this relation is {8, 4, -1}. Easy as pie!

The teacher was impressed with Jack's quick thinking and problem-solving skills. Well done, Jack! You're a math whiz!

And so, Jack saved the day in Math class and became the hero of the hour. The end.

Keywords:

Domain
Range
Relation
X-Value
Y-Value

Wrapping Up: The Wild World of Domains and Ranges

Well folks, we've reached the end of our journey through the strange and mysterious world of domains and ranges. We hope you've enjoyed this wild ride as much as we have!

In this article, we tackled the question of what the range is for the relation 12x + 6y = 24 when the domain is given as {-4, 0, 5}. It might seem like a boring math problem at first glance, but trust us - there's more to it than meets the eye.

First, we had to understand what exactly domains and ranges are. Put simply, the domain is the set of all possible input values for a function or relation, while the range is the set of all possible output values.

Once we had that down, we could start digging into the specifics of this particular problem. By plugging in our given x-values and solving for y, we were able to find that the range for this relation is {-6, 0, 6}.

But wait, there's more! We also explored some of the more esoteric aspects of domains and ranges, such as how they can be used to determine whether a function is one-to-one (meaning each input has exactly one output) or onto (meaning every output has at least one corresponding input).

We even delved into the fascinating world of inverse functions, which are essentially functions that undo another function. To find the inverse of a function, we simply switch the roles of x and y and solve for y.

Now, we know what you're thinking - Wow, this all sounds super exciting, but I'm still not sure how any of it applies to my everyday life. And you know what? Fair point.

But here's the thing: understanding domains and ranges (and inverse functions, and one-to-one vs. onto functions, and all that jazz) is actually incredibly useful in a lot of fields. It can help you analyze data, make predictions, and even design algorithms.

Plus, it's just plain cool to be able to look at a function or relation and know exactly what its domain and range are. You'll be the life of the party, we promise.

So there you have it, folks. We've explored the ins and outs of domains and ranges, solved a tricky math problem, and hopefully learned something new along the way. Thanks for joining us on this journey, and happy math-ing!

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