Discover the Range of Y = -2x + 3 with Domain {0, 2, -6} - A Comprehensive Guide

If The Domain Is {0, 2, -6}, What Is The Range Of Y = -2x + 3?

The range of y = -2x + 3 with domain {0, 2, -6} is {-15, -1, 9}.

Are you ready to dive into the world of mathematics? Brace yourself because we are about to explore the relationship between domain and range! Let's start with a simple question: If the domain is {0, 2, -6}, what is the range of y = -2x + 3?

Before we answer that question, let's quickly review what domain and range mean. The domain is the set of all possible x-values for a given function, while the range is the set of all possible y-values. In other words, the domain represents the input values, while the range represents the output values.

Now, back to our question. To find the range of y = -2x + 3, we need to plug in each value from the domain and see what output we get. Sounds easy enough, right? Let's see if we can make it even easier with some mathematical tricks.

First, let's rewrite the equation as y = -2(x - 3/2). This form is called the slope-intercept form, and it tells us that the slope of the line is -2 and the y-intercept is 3/2. Why is this useful? Well, it means that for every increase of 1 in x, y will decrease by 2. So, if we know the y-value when x is 0, we can easily find the y-values for the other x-values in the domain.

Let's start with x = 0. Plugging this into our equation gives us y = -2(0 - 3/2) = 3. So, our first point on the graph is (0, 3). Now, let's move on to x = 2. Plugging this into our equation gives us y = -2(2 - 3/2) = 4. We can now add another point to our graph: (2, 4).

Finally, let's try x = -6. Plugging this into our equation gives us y = -2(-6 - 3/2) = -9. We can add one last point to our graph: (-6, -9). Now that we have three points on the graph, we can connect them to get a straight line.

But what does this have to do with the range? Well, now that we have the graph, we can easily see what the range is. The lowest y-value on the graph is -9, and the highest y-value is 4. Therefore, the range of y = -2x + 3 when the domain is {0, 2, -6} is {-9, -7, -5, -3, 1, 3, 5, 7, 9, 11}.

Now that you know how to find the range of a function, you can impress your friends with your mathematical prowess. But don't stop here! Keep exploring the fascinating world of mathematics, and who knows what other secrets you might uncover.

Introduction

It's time to put on our math hats and dive into the world of domains and ranges. Specifically, we'll be exploring what happens when a given domain is paired with a particular equation, as in the case of Y = -2x + 3 and the domain {0, 2, -6}. But don't let the math jargon scare you - we'll be approaching this topic with a humorous tone to make it as enjoyable as possible.

What is a Domain?

Before we can dive into the specifics of Y = -2x + 3 and the domain {0, 2, -6}, let's first define what we mean by domain. In math terms, the domain refers to the set of all possible input values for a given equation. Think of it like a menu at a restaurant - the domain lists all the options available for the equation to work with.

The Domain: {0, 2, -6}

Now that we understand what a domain is, let's take a closer look at the specific domain we'll be working with in this article: {0, 2, -6}. This means that the equation Y = -2x + 3 will only be evaluated for these three input values, and not any others.

What is a Range?

Next up, we have the concept of the range. Similar to the domain, the range refers to the set of all possible output values for a given equation. Continuing with our restaurant analogy, the range would be like the dishes that are available to order from the menu.

Solving Y = -2x + 3

Now it's time to actually solve the equation Y = -2x + 3 using the domain {0, 2, -6}. To do this, we simply plug in each of the three input values for x and solve for y. So:

When x = 0: Y = -2(0) + 3 = 3

When x = 2: Y = -2(2) + 3 = -1

When x = -6: Y = -2(-6) + 3 = 15

Putting It All Together

Now that we have our three output values for Y, we can list them out to find the range. In this case, our range is {3, -1, 15}. These are the only possible output values for the equation Y = -2x + 3 when using the domain {0, 2, -6}.

What Does It All Mean?

So, what can we actually take away from all of this? Well, first and foremost, we now know what the range of Y = -2x + 3 is when using the domain {0, 2, -6}. But beyond that, understanding domains and ranges can be incredibly useful in a variety of math-related fields, from statistics to computer science.

The Importance of Humor

We hope that our humorous approach to this topic has made it more enjoyable and accessible for you. Math can often be seen as dry and boring, but it doesn't have to be! By injecting a bit of humor into the mix, we hope to make math a more approachable and less intimidating subject for everyone.

Conclusion

In conclusion, we've explored the concept of domains and ranges and how they relate to the equation Y = -2x + 3. By using the domain {0, 2, -6}, we were able to determine that the range for this equation is {3, -1, 15}. And while math can often seem daunting, we hope that our humorous approach has made it a bit more enjoyable for everyone.

If The Domain Is {0, 2, -6}, What Is The Range Of Y = -2x + 3?

Math and I aren't exactly on speaking terms, so when I saw this question I threw up my hands and yelled, y'all on your own! But then I realized it's my job to help, so here goes nothing...

Prepare to have your mind blown

We're about to navigate the treacherous waters of domain and range. Just kidding, it's actually not that scary, I promise. Forget playground drama, the real beef in life is between domain and range. They just can't seem to get along! Listen up, folks - we're about to figure out what crazy shenanigans the equation y = -2x + 3 is up to with a domain of {0, 2, -6}. Brace yourselves!

Let's break it down

For those of you who have been living under a rock (or just didn't pay attention in math class), the domain is the set of all possible x-values, while the range is the set of all possible y-values. Got it? Good. The equation y = -2x + 3 might sound like gibberish to some of you, but trust me - it's just a fancy way of saying make a bunch of points on a graph and see what happens.

Connect the dots

Now, if we plug in our domain values of 0, 2, and -6, we'll get corresponding y-values. Think of it like a game of Connect the Dots, but with math instead of crayons. And just like that, we have our range - the set of all possible y-values for the equation y = -2x + 3 with a domain of {0, 2, -6}. Want to see it in action? I'll grab my graph paper!

We did it!

Congrats, my math-challenged friends - we made it through another problem! Next up, world domination. Or maybe just a coffee break, your call. I'm not saying domain and range are frenemies, but they definitely keep each other at arm's length. Maybe they just need to hug it out?

The Range of Y = -2x + 3 with Domain {0, 2, -6}

Story Telling

Once upon a time, there was a math problem that needed to be solved. The problem was, If the domain is {0, 2, -6}, what is the range of y = -2x + 3?

Three mathematicians, named Tom, Dick, and Harry, were tasked to solve the problem. Tom said, Let's substitute each value in the domain to the equation and get the corresponding values of y. Dick replied, We can then put those values in a set to get the range. Harry added, And we can use our calculator to make it easier.

They all agreed and started working on the problem. After a few minutes, they got the values of y for each x-value in the domain. They put those values in a set and voila! They got the range of y = -2x + 3.

Tom exclaimed, The range is {-9, -1, 15}! Dick said, We did it, guys! And Harry replied, I knew we could do it.

They high-fived each other and celebrated their victory. They never thought that solving a math problem could be this fun and easy.

Point of View

Humorous Voice and Tone

Well, hello there, math enthusiasts! Are you ready for a mind-boggling problem? Of course, you are! Who wouldn't want to exercise their brain cells, right?

So, let's talk about this problem that involves a domain and a range. Don't worry; we're not talking about a piece of land or a gun's firing distance. We're talking about math here, people!

Now, imagine three mathematicians trying to solve this problem. You know how nerdy they can get, right? But, hey, they're good at what they do, so let's give them a chance.

Tom, Dick, and Harry are their names. I know; it sounds like a children's book. But, trust me, they're not childish when it comes to math. They took the problem seriously and even used their calculator to make their lives easier.

After a few minutes, they got the range of y = -2x + 3. And guess what? They celebrated their victory like they won a lottery or something. I mean, who knew solving a math problem could be this exciting, right?

Table Information

Let's summarize the information we got from the story:

Problem: If the domain is {0, 2, -6}, what is the range of y = -2x + 3?
Mathematicians: Tom, Dick, and Harry
Method: Substitute each value in the domain to the equation and get the corresponding values of y. Put those values in a set to get the range.
Range: {-9, -1, 15}

There you have it, folks! A fun and easy way to solve a math problem. Who said math can't be enjoyable, right?

Bye for now, Math Wizards!

Well, well, well! We’ve come to the end of our mathematical journey. I hope you’re feeling a bit more confident about your math skills and ready to tackle any problem that comes your way. Let’s do a quick recap before we say goodbye.

First, we talked about domains and ranges and how they are used in mathematical functions. We learned that the domain is the set of all possible x-values of a function, while the range is the set of all possible y-values of a function.

Then, we looked at a specific example: If the domain is {0, 2, -6}, what is the range of y = -2x + 3? We walked through the steps of solving for the range and found that the range is {-15, -1, 9}.

Now, I know math can be a dry subject, so let’s inject some humor into this closing message. Did you hear about the mathematician who’s afraid of negative numbers? He’ll stop at nothing to avoid them! 😂 Okay, okay, I’ll stop with the puns.

All jokes aside, I want to encourage you to keep practicing your math skills. Don’t be afraid to ask for help when you need it and remember that making mistakes is a natural part of learning.

Before we go, I want to leave you with a quote from the famous mathematician, Albert Einstein: “Pure mathematics is, in its way, the poetry of logical ideas.” So, go forth and create some beautiful poetry with your newfound math skills!

Thank you for joining me on this mathematical journey. Keep learning, keep growing, and keep solving those equations!

Until next time, Math Wizards!

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