What is the range of the relation plotted on the graph?

Decoding the Range of a Graph: It’s Easier Than You Think!

Okay, so you’ve got this graph, right? Lines, curves, maybe even some scattered dots. It’s all a “relation,” which is just a fancy way of saying things are connected. But how do you figure out what the range is? Don’t sweat it; it’s simpler than it sounds.

Think of the range as the graph’s vertical reach. Seriously, that’s all it is! It’s the total distance the graph covers if you were to measure it from top to bottom. We’re talking about the possible “output” values, the y-values on your graph.

So, how do you actually find this range? Let’s break it down:

First things first, zero in on that y-axis. Remember, the range is all about those vertical values. Next, play “spot the extremes.” What’s the lowest point the graph hits? The highest? Those are your boundaries.

Now, here’s the thing: it’s not just about those highest and lowest points. You need to consider everything in between. Does the graph cover all the y-values between those extremes? Are there any gaps or jumps?

This is where “interval notation” comes in. It’s just a neat way to write down the range. Imagine the lowest point is -2, and the highest is 5, and the graph includes all the values in between. We’d write that as -2, 5. See those square brackets? They mean we’re including -2 and 5 in the range. If, for some reason, the graph didn’t include those endpoints, we’d use parentheses instead. So, (-2, 5) would mean all the values between -2 and 5, but not -2 and 5 themselves.

And what about those graphs that go on forever? If your graph shoots off upwards with no end in sight, we say it goes to infinity (∞). So, if your graph covers all y-values greater than, say, 3, you’d write the range as (3, ∞). Just remember: infinity always gets a parenthesis because you can’t actually “include” infinity.

Let me give you a few quick examples to really nail this down:

• Imagine a nice, neat curve that bottoms out at y = -4 and peaks at y = 3. It covers everything in between. Range: -4, 3.
• Now picture a graph that starts at y = 0 and just keeps climbing forever. Range: 0, ∞).
• What if you just have a straight horizontal line at y = 2? Well, the range is simply {2}. That’s it!
• And for something a little different, suppose you only have a few scattered points: (1, 2), (3, 4), and (5, 6). The range is just the y-values of those points: {2, 4, 6}.

Now, a word of warning: don’t mix up the range with the domain. The domain is all about the x-values, the horizontal spread of the graph. Think of it this way: domain is “left to right,” range is “bottom to top.”

Also, remember that while we can find the range for any relation, it’s especially important when we’re talking about functions. Functions are special relations where each x-value has only one y-value. You can use the vertical line test to quickly check if a graph represents a function. (Basically, if a vertical line ever crosses the graph more than once, it’s not a function.)

So, there you have it! Finding the range of a graph is all about spotting those y-values, understanding how the graph behaves vertically, and using that interval notation like a pro. Once you get the hang of it, you’ll be decoding graphs left and right!


of it, you’ll be decoding graphs left and right!