
Discontinuities and Derivatives in Functions

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned

Ethan Morris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What type of discontinuity is characterized by a gap in the graph where the function jumps from one value to another?
Oscillating discontinuity
Infinite discontinuity
Jump discontinuity
Removable discontinuity
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following statements is true about a function that is continuous but not differentiable at a point?
The function is not defined at that point.
The function has a sharp turn at that point.
The function has a vertical asymptote at that point.
The function has a hole at that point.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For a piecewise function to be continuous at a point, what must be true about the limits from the left and right?
They must be undefined.
They must be equal to each other.
They must be positive.
They must both be zero.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If a function is not continuous at a point, what can be said about its differentiability at that point?
It is differentiable only if the function is linear.
It is never differentiable.
It is always differentiable.
It may or may not be differentiable.
Tags
CCSS.8.EE.B.5
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the slope of the line y = x + 2?
2
3
0
1
Tags
CCSS.HSF-IF.C.7B
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of piecewise functions, what does a smooth transition between two segments indicate?
The function is not continuous.
The function is differentiable.
The function has a jump discontinuity.
The function is undefined.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of x^3?
2x
3x^2
3x
x^2
Tags
CCSS.HSF-IF.C.7D
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