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You are watching: Does the table describe a function
To compose a duty to describe a table of worths, initially view if tbelow are any patterns that present up best away. If not, then take into consideration the slope-intercept create of a line y=mx+b, wright here m = slope and b = y-intercept. The y-intercept is the suggest wright here the line crosses the y-axis. At that allude, the coordinate points would have a x value of 0. Therefore, in the table of worths, if tbelow is a pair of values in which the x is 0, then that ordered pair represents the suggest wbelow the graph of the function crosses the y-axis, or the y-intercept, which is "b". Next off, to uncover the slope, use the slope formula and plug in the values from two ordered pairs from the table of worths as the x1, y1 and x2, y2 values. Since slope is basically the change in the x-value over the change in the y-value, you deserve to additionally find the slope by determining the unit of change for the x and also y. Once you find the worth of the slope, plug it right into the slope-intercept develop of the line. The result is the function that defines the relationship in the provided table of worths. Make certain it is equal to f(x).
This trouble is a little little complicated because when you're looking at these variety of boxes you deserve to watch it's decreasing. I start out via 1, 2, 3, 4, times 4. I begin through 16 boxes then I come dvery own to just 12 and then 8 and then 4. So it's a tiny bit different from some of the troubles that you might have actually checked out because these numbers are decreasing rather of boosting. The pictures are gaining smaller sized. So what I desire to execute is look for some sort of patterns, view if I deserve to check out anything that I deserve to recognize as a mathematical pattern that I'm acquainted via. Like for example in order to help me organize this, I'm going to make a table wright here I have photo number and then number of boxes and that's going to aid me look for trends. Like my picture numbers are 0, 1, 2, 3 and also 4, 0, 1, 2, 3 and 4 and also then if you count up just how many kind of boxes tbelow are at 16, then we have 12, then we have 8 and also then 4 and then this fourth photo has zero boxes. It's kind of weird we'll resolve it once we obtain to it. Okay so that's simply one more method of representing the very same indevelopment and I have to discover an equation that defines this. So I'm going to begin by writing an equation in words and also I'll go and readjust it into mathematical signs in a second. Number of boxes is going to be equal to something.Well one thing I notice is that I'm beginning via 16, my zero group started with 16 from tbelow it's decreasing. So I'm going to say 16 take ameans somepoint I don't know what's going to go there yet. Then let's look at how a lot it's going dvery own by. Each time I'm subtracting 4 boxes, choose I used to have 4 rows of 4 or four columns of four currently I only have three columns of 4, that's the one that acquired taken away. Here aobtain I'm taking away a column of 4 boxes from the previous photo. What's happening is I'm subtracting 4 eincredibly time. You can check out it here, take away 4, take amethod 4 and also on and on and on. So the means this pattern would certainly be created would be -4 times the image number, picture number. That's exactly how I would write it in words or if I wanted to usage mathematical symbols I would 16 take amethod 4x that dominance or that equation explains exactly how many kind of boxes tright here are in each photo number.So aget this one's sort of weird bereason rather of gaining bigger the photos are obtaining smaller however you can still usage your pattern approaches.
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Look for where you're starting from and also then look at how a lot you're changing by. We started with 16 and then we're decreasing by 4 each time.