8,706, 2812 What is the value of 7
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The piecewise function is basically the result of two different functions combined together. If x is 0 or larger, then h(x) = x+4. Otherwise, if x < 0, then h(x) = -x-4
No matter what number you pick for x, the h(x) function will be used in some way. So the domain is the set of all real numbers. To write this in interval notation, we write which means we start off at negative infinity and go to positive infinity. This is basically saying "the entire real number line". Since we can't actually reach either infinity, we always use parenthesis with them. <u>Never</u> use square brackets with either infinity
From the graph (see attached image below), we see that (0,-4) is the lowest point. This means y = -4 is the smallest y output possible, though we can't actually reach it because of the open circle at (0,-4). We can get any other larger y value. So the range is therefore: meaning we start at -4 and head off to positive infinity. The curve parenthesis next to -4 the reader "exclude -4 as part of the range". There is an open hole or gap here. Another way to state the range is to write y > -4
In similar figures, the angle measures are the same but the side lengths are different. So in #4, x = 42. Since all the angles of a quadrilateral added up equal 360, then y is 360-90-90-42=138. For number 5, make sure you match up the sides correctly in your ratio: 
. You could cross multiply to get 4x=16, and x = 4, or you could just realize that reducing 4/8 will give you 2/4 and x = 4. Going back to the idea that in similar shapes corresponding angles are the same measure, x in #6 is 63