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Question 1096471: Hi, earlier I posted my math problem but I couldn’t figure out how to upload the image so you can see what I’m talking about. This is what I’m struggling with!
https://imgur.com/a/JfxhF
Answer by greenestamps(13196)   (Show Source):
You can put this solution on YOUR website!
Part I: Increasing and decreasing.
When we talk about a function increasing or decreasing, we are talking about whether the function value is increasing or decreasing as the value of x increases. For many students (and for me), a convenient way to think about it is that I am walking from left to right on the graph (so that x is increasing), and I want to know whether I am going up (function is increasing) or down (function is decreasing).
In your example, with a minimum at (7.5, -0.25), you are always going down (the function is decreasing) as long as you are to the left of the minimum; and you are always going up (the function is increasing) as long as you are to the right of the minimum.
So the function is decreasing on the interval from -infinity to 7.5 and increasing on the interval from 7.5 to infinity.
Part II: Domain and range.
The domain is the set of x values for which the function is defined; the range is the set of y values (that is, function values) that the function can have.
For the domain, you can't really tell from the graph; however, you have to assume that you can go as far as you want to the right or left and you will still be somewhere on the graph. So there are no restrictions on the values of x; the domain of the function is all real numbers, from -infinity to +infinity.
The range is easier in this case. The minimum value of the function is -0.25; and again there clearly is no limit to how large the function value can become. So the range of the function is from -0.25 to +infinity.
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