Q
"(i) Identify the domain and range.
(ii) Does this graph represent a function and a one-one function? Why/Why not? Provide a detailed explanation/justification."
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Answer
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Step 1(i) To identify the domain and range of the given graph, we first need to observe the graph and find the values of x and y that it takes.
Therefore, the range is [2, $\infty$).
The graph given in the problem is:  From the graph, we can see that the graph is a parabola opening upwards. The parabola extends indefinitely along the positive y-axis, so the domain is all real numbers greater than or equal to the x-value of the vertex. To find the range, we need to find the minimum value of y. Since the parabola opens upwards, the minimum value of y occurs at the vertex. The y-coordinate of the vertex is y = f(2$) = 2. (ii) To determine if the graph represents a function, we need to check if each x-value corresponds to only one y-value. In this case, the graph is a parabola, which is a function because each x-value corresponds to only one y-value. To determine if the function is a one-to-one function, we need to check if each y-value corresponds to only one x-value. In this case, the graph is a parabola, which is not a one-to-one function because there are two x-values that correspond to the same y-value at the vertex. Therefore, the graph represents a function but not a one-to-one function.
Final Answer
(i) The domain of the graph is [$- 2, \infty$) and the range is [2, $\infty$). (ii) The graph represents a function but not a one-to-one function.
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