a) State the three conditions of continuity of a function f (x) at a point x=c b) find the value of the constant k that makes the function f(x) continuous at x=5 f(x)= kx+3; x greater than or equal to 5 f(x)=3x+k; x is less than 5 Be sure to use each condtion of continuity

Determine where the function m(x) = X+1 (x-1)(x-4) is continuous. The function is continuous on (Simplify your answer. Type your answer in interval notation.)

Sketch the given functions on a graph then answer the following questions: f(x)= 4-x for x < -2 f(x)= 2x+3 for -2 < x < 3 f(x)= -x for x > 3   1.) is this function continuous where x=3? Explain why or why not using the definition of continuity. (3 requirements that must be met) 2.) Where is the function right side continuous? 3.) Where is the function left side continuous?

Determine the values of x where the function f(x) is not continuous. Label each discontinuity as removable, jump or infinite.  Problem is in picture, thank you!