Kevin packs cans of beans into cases. He has 3,987 cans, and each case holds 240 cans. How many cases will he need to pack all t
2 answers:
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Answer:
See below.
Step-by-step explanation:
So we have the graph of:
As given, the graph is a circle with a radius of 2√2 and a center of (0,0)
Part 1)
The domain of a function is the span of x-values it covers and the range of a function is the span of y-values it covers.
From the graph, we can see that the x-values the graph covers goes from -2√2 to +2√2. The graph includes these values.
Thus, the domain is, in interval notation:
From the graph, we can see that the y-values the graph covers also goes from -2√2 to 2√2.
Therefore, like the domain, the range in interval notation is:
Part 2:
First of all, we can use the vertical line test to prove that the graph is indeed not a function.
Algebraically, we have to do some more.
First, recall what it means when an equation is not a function. It means that one x maps onto two or more ys.
In other words, to prove that the equation is not a function, we can substitute an x for a value and solve for y.
For instance, let's use 0 for x (and 0 is within the domain). Thus:
Simplify:
Take the square root of both sides:
In other words, when x is 0, y can be either -2√2 or 2√2. So we have two different y-values with the same x-coordinate.
Therefore, the equation is not a function.