Answer:
A) Notice that the given function is the function absolute value translated 1 unit to the right, dilated by a factor of 1/2, reflected over the x-axis, and finally, translated two units up. Therefore
[tex]y=-\frac{1}{2}|x-1|+3[/tex]has a vertex with coordinates:
[tex](1,3)\text{.}[/tex]B) Since the vertex is at (1,3), the graph has an axis of symmetry with equation:
[tex]x=1._{}[/tex]C) The t-chart and the graph of the equation are as follows:
