Final answer:
The domain of the given point set is {0, 1, 3, 5, 10}, and the range is {-10, -2, 1, 2, 5}. A mapping diagram would show one-to-one connections between each element of the domain and range. The function is one-to-one because each input is paired with a unique output.
Step-by-step explanation:
List the Set of Domain and Range
The domain of a function is the set of all possible input values (x-values) for which the function is defined. When listing these values from the given point set {(5,-10), (3,-2), (10,5), (0,1), (1,2)}, we order them from smallest to largest and only list an element once if it appears multiple times. The domain for this point set is {0, 1, 3, 5, 10}.
The range of a function is the set of all possible output values (y-values), which result from using the function's formula. Similarly, we list these from smallest to largest without repetition. The range for this point set is {-10, -2, 1, 2, 5}.
Draw the Mapping Diagram
To draw a mapping diagram, we would sketch two parallel columns of points with the domain on the left and the range on the right, and then draw one-to-one arcs connecting each point in the domain to its corresponding point in the range according to the given set of points.
Is this a One-to-One Function?
A one-to-one function is one in which each element of the domain is paired with a unique element of the range. In other words, no two distinct elements in the domain map to the same element in the range. In this case, since each x-value is paired with a different y-value, the function represented by the given point set is indeed a one-to-one function.