1- The following function is one-to-one
f(x)= -x if x belongs to [-1,0]
f(x)=3x+2 if x belongs to [0,1]
2- The following parametric curve represents a line segment from (0,3) to (2,0) :
For (1): I think its false, if we draw the function on the interval [-1,1] we will get a graph which is similar to the graph of f(x)=|x| (the v-shape). clearly there are horizontal lines intersect the curve of f in more than one point, so its not 1-1 function, so the statement is false.
For (2): I do not have any idea!