A.P. Calculus
Continuity and Differentiability
Name _________________________
1) What is the informal definition of a continuous function?
2) What is the formal definition of a continuous function?
Open the TI-Nspire document Continuity_and_Differentiability
v2.tns.
Objective: To determine when a function is continuous or
differentiable.
Directions: Follow directions in the TI-Nspire document to
determine when the given functions are continuous and/or
differentiable.
Move to page 1.2.
Press /
¢ and / ¡ to navigate
through the lesson.
3) What is a cusp? How is it related to determining whether a function is
differentiable?
4) Sketch your graph of #1 (include
the equation) after you have made
this piece-wise function continuous.
What is the value of the constant that you
found worked?
Substitute the values of x and a in the
piece-wise function. What do you notice
about the answers in this case?
A.P. Calculus
Continuity and Differentiability
5) Sketch your graph of #2 (include
the equation) after you have made
this piece-wise function continuous.
Name _________________________
What is the value of the constant that you
found worked?
Substitute the values of x and a in the
piece-wise function. What do you notice
about the answers in this case?
6) Sketch your graph of #3 (include
the equation) after you have made
this piece-wise function continuous.
What is the value of the constant that you
found worked?
Substitute the values of x and a in the
piece-wise function. What do you notice
about the answers in this case?
A.P. Calculus
Continuity and Differentiability
7) Sketch your graph of #4 (include
the equation) after you have made
this piece-wise function continuous.
Name _________________________
What is the value of the constant that you
found worked?
Substitute the values of x and a in the
piece-wise function. What do you notice
about the answers in this case?
8) Sketch your graph of #5 (include
the equation) after you have made
this piece-wise function continuous.
What is the value of the constants that you
found worked?
Substitute the values of x, c and d in the
piece-wise function. What do you notice
about the answers in this case?
A.P. Calculus
Continuity and Differentiability
9) Sketch your graph of #6 (include
the equation) after you have made
this piece-wise function continuous.
Name _________________________
What is the value of the constants that you
found worked?
Substitute the values of x, c and a in the
piece-wise function. What do you notice
about the answers in this case?
10) Sketch your graph of #7 (include
the equation) and describe how this
function is different than the
previous problems.
What is the value of the constant that you
found worked?
Substitute any values of x and a that you
inspected for this piece-wise function.
What do you notice about the answers in
this case?