Since it's so nicely grouped, we can work with it! For the equation to equal 0, x=0, 3, or -1 (since x-3 and x+1 equal 0 when plugged in with 3 and -1 respectively). All we have to do is plug in numbers before, between, and after these numbers and apply it to the rest of them. Since -1 is the smallest number of the group, we can plug in a number below that (for this example, -5) and plug it in to get -8*-5*-4= something negative since it contains an odd number of negative numbers. Therefore, anything less than 1 is negative. For between -1 and 0, we get x=-0.5 equals -0.5*-3.5*0.5=something positive (since it has an even amount of negative numbers), proving that everything between -1 and 0 here is positive. For something between 0 and 3, we can plug 1 in to get 1*-2*2= something negative. Do you see a pattern here? It's negative, then positive, etc.. Therefore, if the number is greater than 3 it is positive. Reviewing a bit, we can see that (-inf, -1) is negative as well as (0,3), making the interval notation (-inf, -1) U (0, 3) since when you plug -1, 0, and 3 in it is 0, not less than 0!
notice how u have the same y values of 0....this means u have a horizontal line where no matter what x is, y will always be 0. A horizontal line has a slope of 0. And ur y intercept is (0,0)
the linear function that is in the table contains a negative slope and also has a steeper slope then the one on the coordinate plane <===
Vertical lines take the form of and horizontal lines take the form of
Why is this? Notice that whenever you make a horizontal line on a graph and select virtually any point that's on that line, all of the points you pick will have the same y value. Try to imagine the same thing with a vertical line, are the results the same?
So the line (we got -12 from the coordinate that was given to us on the question prompt) is a vertical line that passes through virtually all possible y values (from positive infinity to negative infinity, or vice-versa) which means that the question prompt having given us the y value was negligible.
