Let \( A(k) \) be the area bounded by the curves \( y=x^{2}-3 \) an...

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Let \( A(k) \) be the area bounded by the curves \( y=x^{2}-3 \) and \( y=k x+2 \).
\( \mathrm{P} \)
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(1) The range of \( A(k) \) is \( \left[\frac{10 \sqrt{5}}{3}, \infty\right) \)
(2) The range of \( A(k) \) is \( \left[\frac{20 \sqrt{5}}{3}, \infty\right) \)
(3) If function \( k \rightarrow A(k) \) is defined for \( k \in[-2, \infty) \), then \( A(k) \) is many-one function
(4) The value of \( k \) for which area is minimum is 1
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