The vertical line test can be used to determine if the graph of a curve is a function. The vertical line test determines if for every value of x there is only one value of y corresponding to it.[br][br]The graph shows the function [math]h(x)=sin^2(x)+x[/math], and the line [math]x=a[/math]. By adjusting the values of [math]a[/math], check that [math]h(x)[/math] passes the vertical line test, i.e. for every value of [math]x[/math] there is only one value of [math]y[/math] corresponding to it.

What about the graph below, does it pass vertical line test? [br][br]Is this graph representing a function? Explain why.

Can you think of what features a curve must have to be the graph of a function? Perhaps contrast these two graphs.