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3 years ago

I don't get this at all

Mathematics

1 answer:

Anna007 [38]3 years ago

8 0

Δy/Δx is nothing but the slope and slope = rise/run .

Look up in the FIRST graph; From the lower point on the line draw a // to x-axis and from the higher point draw a // to y-axis. Note the point of intersection, their coordinates are (6, 3) [ x=6 = run and y= 3 = rise)
Or Δy = rise = 6 and Δx = run = 3, hence Δy/Δx = 6/3 = 1/2 = slope.

Do the same thing with the 2nd graph:
Δy = 3 and Δx = - 2 (you are counting from right to left), then

Δy/Δx = 3/(-2) and Δy/Δx = -3/2

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For finding the values, we look at the x - value given. Then we move to where it is on the graph and find its y value.

In part A, when x = -4, the y value looks to be between -3 and -4. Let's put it in the middle and estimate it at -3.5

In part B, when x = 1, the process is similar. Go to x = 1, then go to the graph, then go to the y value. That looks to be at y = -3.

In part C, when x = 4, there are three values that work. We are actually answering part D at this point because we can tell this graph is NOT a function of x. When you have an x -value that goes into the function, you have to get EXACTLY ONE thing that comes out. I bolded "EXACTLY ONE" because those words make the definition work. Two or more, not a function. One, it's a function. None, and it's not in the domain at all. There are three values of y that work, and they are - from top down, 3.5, 0, -2.5.

We answered Part D when observing part C. It's NOT a function because there is not EXACTLY ONE value of y for an x.

And finally, because it's not a function - finding the domain and range is a waste of time. You can't find the domain of something that's not a function - you need a function to have a domain.

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