Functions and Graphs, SMB-008 A function has the equation `f(x)=4-(x+1)^2`. State the domain and range of `f(x)`. (3 marks) Show Answers Only `text{Domain}\ f(x): \ text{all}\ x` `text{Range}\ f(x): \ y<=4` Show Worked Solution `f(x)\ text{exists for all}\ x` `text{Domain}\ f(x): \ text{all}\ x` `text{Consider the function transformation:}` `y=x^2\ text{translated 1 unit left}\ =>\ \ y=(x+1)^2` `y=(x+1)^2\ text{reflected in the}\ xtext{-axis}\ =>\ \ y=-(x+1)^2` `y=-(x+1)^2\ text{translated 4 units up}\ \ =>\ \ y=4-(x+1)^2` `:.\ text{Range}\ f(x): \ y<=4`