10. How to tell whether a given graph in rectangular coordinates represents a function.(a) Given a graph in rectangular coordinates, how do we tell whether the graph represents a function?(b) Given a graph in polar coordinates, how might we tell whether the graph represents a function?(c) Using a graphing calculator or Desmos, graph r(θ) = 3cos(2.1θ). Does this graph represent a function? Justify your answer. 10. Recall that at the beginning of the semester we spoke about how to tell whether agiven graph in rectangular coordinates represents a function.(a) Given a graph in rectangular coordinates, how do we tell whether the graphrepresents a function?(b) Given a graph in polar coordinates, how might we tell whether the graphrepresents a function?(c) Using a graphing calculator or Desmos, graph r(0) = 3cos(2.10). Does thisgraph represent a function? Justify your answer.

Given Data: Let us consider the given data, (a) Given a graph in rectangular coordinates, how do we tell whether the graph represents a function. (b) Given a graph in polar coordinates, how might we tell whether the graph represents a function. (c) Using a graphing calculator or Desmos, graph r =3 cos 2.1 θ. Does this graph represent a function.Solution: Function: A function f: A→B is a rule from A to B that assigns each element of A to exactly one element of B. (a) Suppose equation of given graph is gx,y,z=0. If for any pair x,y value of z is unique , then this graph represents a function otherwise not. For Example: Graph of sphere x2 +y2 +z2=1 can not represents a function as for x,y =12,12 value of z=±12 (not a unique value)(b) Suppose , equation of given graph is hr,θ =0 if for any value of θ , value of r is unique , then this represents a function otherwise not. For Example: r=θ ,0≤θ≤π is a function but r2 =θ ,0≤θ≤π is not a function as θ=π2 ,r=±π2 (not a unique value) (c) Graph of r =3 cos 2.1 θ This represents a function as there is no value θ =θ0 for which r has two distinct values.