Answer:
7. domain: x ≤ 5; range: y ≥ -5; "starting point": (5, -5)
8. B. y = √(-(x-2))
Explanation:
7.
The domain is the horizontal extent of the graph. The arrow at the left end of the curve indicates it extends to -∞. The right end of the curve ends at the point (x, y) = (5, -5). So, the graph extends horizontally from -∞ to 5. In interval notation, this is written (-∞, 5]. As an inequality, the domain is written ...
x ≤ 5
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The range is the vertical extent of the graph. As with the domain, the arrow at the end of the curve means it extends upward to ∞. The curve extends downward to -5, so the range is [-5, ∞) or y ≥ -5.
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We're not sure how you're defining "starting point" in this situation. It is convenient to think of the end of the curve that has finite coordinates as being its "starting point." If that is the point you're looking for, it is (5, -5).
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8.
The table shows x decreasing as y increases. This mean the coefficient of x will be negative, eliminating choices C and D. Perhaps the easiest way to determine whether A or B is the equation is to try it. Square and cube roots are the same for arguments 0 and 1, so it is convenient to use a different point, such as x=-2. Then you get ...
A: y = ∛(-(-2-2)) = ∛4 ≠ 2
B: y = √(-(-2-2)) = √4 = 2
The equation of the table is ...
y = √(-(x -2))
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Additional comment
As far as we know, the term "starting point" is not rigorously defined in Algebra. For functions that have a practical domain whose minimum value is zero, the y-intercept of the graph is often referred to as the "starting value". Sometimes that term is used for the y-intercept even if the domain is infinite in both directions.
When the domain is a closed interval, or a semi-infinite interval extending indefinitely to the right, the "starting point" might be its left end, the minimum x-value. Here, we have chosen to use that notion for a semi-infinite domain extending indefinitely to the left. That is, we have taken the "starting point" to be the maximum x-value.
In the context of problem 7, it does not really make much sense to claim the y-intercept ≈ (0, -2.764) as the starting point.