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Describing Domain and Range

Describing Domain and Range 1.2 - Solution

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a

The domain is all allowed xx-values of a function. In the coordinate system we find the domain by examining for which xx-values the function is graphed. Graph AA doesn't have any endpoints, which means that it's defined for all x,x, so it should be paired with domain 3.3. Graph BB is drawn between x=-6x=\text{-} 6 and x=2.x=2.

This can be written as -6x2\text{-} 6 \leq x \leq 2, which is domain 2.2. Graph CC is plotted from x=-2x=\text{-} 2 to x=3,x=3, where the point at x=-2x=\text{-} 2 is not closed. This means that the function is defined for each value before, but the xx-value of the actual point is not included.

Thus, xx must then be greater than -2\text{-}2 and less than or equal to 3.3. This is written as -2<x3,\text{-} 2 < x \leq 3, which is domain 1.1. In conclusion, 1C,2B,3A. 1-C,\quad 2-B,\quad 3-A.

b

The range of a function can be derived from the yy-values of the plotted graph. Graph AA has no lower or upper limit, which means the range is all y,y, range 3.3. Graph BB has its maximum value at the left-hand endpoint, where y=4,y=4, and its minimum value at the other endpoint, where y=-3y=\text{-} 3.

Then range is, thus, -3y4,\text{-} 3 \leq y \leq 4, range 1.1. Graph CC has its maximum value at the right-hand endpoint, where y=6.y=6. Its minimum value is where y=-3.y=\text{-}3.

Therefore, the range is -3y6,\text{-} 3 \leq y \leq 6, which is range 2.2. In summary, we have 1B,2C,3A. 1-B,\quad 2-C,\quad 3-A.