Extended real-valued functions with uniform sublevel sets are an important tool for scalarization in nonlinear functional analysis, vector optimization and mathematical economics since they can represent orders, preference relations and other binary relations. In this chapter, ways to construct such functions with desired properties are studied. Moreover, each extended real-valued function will be proved to be the restriction of some function with uniform sublevel sets to a hyperspace. One effect is the characterization of continuity by the epigraph of the function.