Piecewise Function

[johnjones]

Let f(x) { squareroot x if x <= 3
mx + 3/2 if x > 3

What value of m will make this a continuous function (the two pieces of the graph are joined)? How do I tackle this problem? :shock:

 

[stapel]

What is the value of each part of the function when x = 3? (Yes, the second part doesn't allow for x = 3, but it could, since x = 3 doesn't cause division by zero or anything.)

Set the value (for the first half) and the expression (for the second half) equal to each other, and solve (since, to be continuous, the two halves have to meet at x = 3).

Eliz.

 

[Daniel_Feldman]

Hint: for it to be continuous, the limit from the right side must equal the limit from the left side (as x approaches 3).