The graph of \( h(x)= \pm \sqrt{x-3} \) is shown below. A is the \( x \)-intercept of \( h \). 5.1 Give a reason why \( h \) cannot be classified as a function. 5.2 . Determine the coordinates of \( A \), the \( x \)-intercept of \( h \). 5.3 . Write down the domain of \( h \). 5.4 Determine the equation of \( h^{-1}(x) \). 5.5 . Write down a restriction of the domain of \( h^{-1}(x) \) so that \( h \) can become a function. 5.6 Draw the graph of \( h(x) \) and \( h^{-1}(x) \) with the restriction in 5.5, indicating all intercepts as well as the line of symmetry.

The graph of \( h(x)= \pm \sqrt{x-3} \) cannot be classified as a function because a function can only have one output (y-value) for each input (x-value). In this case, the positive and negative square roots imply that for certain values of \( x \) (specifically \( x \geq 3 \)), we have two different outputs: one for \( +\sqrt{x-3} \) and another for \( -\sqrt{x-3} \). This creates a vertical line test failure, confirming that \( h(x) \) does not meet the criteria of a function. To find the \( x \)-intercept \( A \), we set \( h(x) = 0 \). Thus, we have \( 0 = \pm \sqrt{x-3} \). This equation holds true when \( \sqrt{x-3} = 0 \), leading us to \( x - 3 = 0 \) or \( x = 3 \). Therefore, the coordinates of point \( A \), where the curve intersects the x-axis, are \( (3, 0) \).