Functions and Graphs, SMB-010 A function has the equation `h(x)=-1-(x-3)^2`. State the domain and range of `h(x)`. (2 marks) --- 4 WORK AREA LINES (style=lined) --- Show Answers Only `text{Domain}\ h(x):\ text{all}\ x` `text{Range}\ h(x):\ y<=-1` Show Worked Solution `h(x)\ text{exists for all}\ x` `text{Domain}\ h(x):\ text{all}\ x` `text{Consider the function transformation:}` `y=x^2\ text{translated 3 units right}\ \ =>\ \ y=(x-3)^2` `y=(x-3)^2\ text{reflected in the}\ xtext{-axis}\ =>\ \ y=-(x-3)^2` `y=-(x-3)^2\ text{translated 1 unit down}\ =>\ \ y=-1-(x-3)^2` `:.\ text{Range}\ h(x): \ y<=-1`