The use of the vertical line test determines if a line equation is a function. If the vertical line intersects only 1 point, the line equation is a function. If the vertical line intersects more than 1 point, the line equation is not a function.

The functions f and g are defined as follows: Where λ is a constant. (i) Given that gf exists, find the largest value of λ. In the rest of the questions, use the value of λ found in part (i). (ii) On the same diagram, sketch the graph of , and , showing clearly the relationship between the graphs. […]

Two functions f and g are defined as follows: Determine, with reasons, whether fg and gf exist. If the composite function exists, give the rule, domain and range in exact form.