To determine whether a
piecewise function is continuous or discontinuous, in addition to checking the boundary points, we must also check whether each of the functions that make up the piecewise function is continuous.
Given a piecewise function, determine whether it is continuous.
Determine whether each component function of the piecewise function is continuous. If there are discontinuities, do they occur within the domain where that component function is applied?
For each boundary point
of the piecewise function, determine if each of the three conditions hold.
Determining whether a piecewise function is continuous
Determine whether the function below is continuous. If it is not, state the location and type of each discontinuity.
The two functions composing this piecewise function are
on
and
on
The sine function and all polynomial functions are continuous everywhere. Any discontinuities would be at the boundary point,
At
let us check the three conditions of continuity.
Condition 1:
Because all three conditions are not satisfied at
the function
is discontinuous at
A continuous function can be represented by a graph without holes or breaks.
A function whose graph has holes is a discontinuous function.
A function is continuous at a particular number if three conditions are met:
Condition 1:
exists.
Condition 2:
exists at
Condition 3:
A function has a jump discontinuity if the left- and right-hand limits are different, causing the graph to “jump.”
A function has a removable discontinuity if it can be redefined at its discontinuous point to make it continuous. See
[link] .
Some functions, such as polynomial functions, are continuous everywhere. Other functions, such as logarithmic functions, are continuous on their domain. See
[link] and
[link] .
For a piecewise function to be continuous each piece must be continuous on its part of the domain and the function as a whole must be continuous at the boundaries. See
[link] and
[link] .
Section exercises
Verbal
State in your own words what it means for a function
to be continuous at
Informally, if a function is continuous at
then there is no break in the graph of the function at
and
is defined.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills