- How do you know if a graph is continuous?
- Is a graph continuous if it has a hole?
- Where is a function continuous but not differentiable?
- Why does a function have to be continuous to be differentiable?
- What is a continuous graph?
- Can a discrete function be continuous?
- How can I tell if a function is discrete or continuous?
- Can a function be continuous and not differentiable?
- What does it mean for a function to be continuous?
- Is a graph continuous at a sharp point?
- Do removable discontinuities have limits?
- Is Money discrete or continuous?
- Is phone number discrete or continuous?
How do you know if a graph is continuous?
A function is continuous when its graph is a single unbroken curve …
that you could draw without lifting your pen from the paper..
Is a graph continuous if it has a hole?
The function is not continuous at this point. This kind of discontinuity is called a removable discontinuity. Removable discontinuities are those where there is a hole in the graph as there is in this case. … In other words, a function is continuous if its graph has no holes or breaks in it.
Where is a function continuous but not differentiable?
In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass.
Why does a function have to be continuous to be differentiable?
Until then, intuitively, a function is continuous if its graph has no breaks, and differentiable if its graph has no corners and no breaks. So differentiability is stronger. A function is only differentiable on an open set, then it has no sense to say that your function is differentiable en a or on b.
What is a continuous graph?
Continuous graphs are graphs that appear as one smooth curve, with no holes or gaps. Intuitively, continuous graphs are those that can be drawn without lifting a pencil.
Can a discrete function be continuous?
For infinite, you may use the equivalent definition of continuity by Heine: “A is limit of f in accumulation point a iff for each sequence an tending to a, the limit f(an) is A”, so actually a discrete function can be continuous.
How can I tell if a function is discrete or continuous?
A discrete function is a function in which the domain and range are each a discrete set of values, rather than an interval in R. … The function is continuous, as there is no restriction on the values which may be input for x.Mark earns $7.15 in each hour he works. … Mark’s income after 40 hours will be $7.15⋅40=$286.00.Aug 2, 2016
Can a function be continuous and not differentiable?
In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.
What does it mean for a function to be continuous?
In mathematics, a continuous function is a function that does not have any abrupt changes in value, known as discontinuities.
Is a graph continuous at a sharp point?
A function can be continuous at a point, but not be differentiable there. In particular, a function f is not differentiable at x=a if the graph has a sharp corner (or cusp) at the point (a, f (a)). If f is differentiable at x=a, then f is locally linear at x=a.
Do removable discontinuities have limits?
Removable discontinuities are characterized by the fact that the limit exists. Removable discontinuities can be “fixed” by re-defining the function. The other types of discontinuities are characterized by the fact that the limit does not exist.
Is Money discrete or continuous?
A continuous distribution should have an infinite number of values between $0.00 and $0.01. Money does not have this property – there is always an indivisible unit of smallest currency. And as such, money is a discrete quantity.
Is phone number discrete or continuous?
It is also a discrete variable because one can simply count the number of phone calls made on a cell phone in any given day. The possible numbers are only integers such as 0, 1, 2, … , 50, etc….Example 1.11 Variables.NumberVariableType of Variable2What is your height?Measurement and Continuous3 more rows