Question #11fb2 Calculus Limits Continuous Functions 1 Answer Jim H Feb 14, 2017 Please see below. Explanation: Because #f(-2)# is not defined, the function is not continuous in any way at #-2#. #f(0) = 0# but #lim_(xrarr0)f(x)# does not exist. (The left and right limits are different.) Because #lim_(xrarr0^-)f(x) = 0 = f(0)#, #f# is continuous from the left at #0#. Answer link Related questions What are continuous functions? What facts about continuous functions should be proved? How do you use continuity to evaluate the limit #sin(x+sinx)# as x approaches pi? How do you find values of x for which the function #g(x) = (sin(x^20+5) )^{1/3}# is continuous? How do you find values of x where the function #f(x)=sqrt(x^2 - 2x)# is continuous? How do you use continuity to evaluate the limit sin(x+sinx)? Given two graphs of piecewise functions f(x) and g(x), how do you know whether f[g(x)] and... How do you find the interval notation to prove #f(x)= x/(sqrt(1-x^2))# is continuous? How do you use continuity to evaluate the limit #(e^(x^2) - e^(-y^2)) / (x + y)# as #(xy)#... How do you show that the function #f(x)=1-sqrt(1-x^2)# is continuous on the interval [-1,1]? See all questions in Continuous Functions Impact of this question 1468 views around the world You can reuse this answer Creative Commons License