MindMap Gallery Functions and Limits
Postgraduate entrance examination for advanced mathematics functions. A function is a special mapping relationship, which maps each element in a set (definition domain) to a unique element in another set (value range).
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This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
Functions and Limits
function
definition
Two elements: definition domain and corresponding rules
Common functions
rounding function
Properties: x-1<=[x]<=x
Common elementary functions
Memorize the graphs and properties of each function
Power function
exponential function
Logarithmic function
Trigonometric functions
inverse trigonometric function
summary
Composite function
Condition: The range of the inner function is contained in the range of the outer function
Note: Composition of piecewise functions
660 Question 2
The key is which segment of the outer function the function value of each segment of the inner function corresponds to.
Inverse function
Note: Only functions corresponding to single values have inverse functions (one x corresponds to one y)
properties of functions
Monotonicity
Judgment method
Definition of monotonicity
The latter term minus the previous term
Divide the last item from the previous one
Determining the positivity or negativity of the first derivative
Frequently asked questions: Prove or judge monotonicity, find limits (a monotonic bounded function must have a limit)
parity
odd function
Definition: f(-x)=-f(x)
Properties: The graph is symmetrical about the origin, and if it is defined at x=0, there must be f(x)=0
Determine parity
even function
Definition: f(x)=f(-x)
Properties: The graph is symmetrical about the y-axis
Determine the parity of a function
Boundedness
Scored the most
definition
There is an upper bound
There is a lower bound
Necessary and sufficient conditions for being bounded: there is both an upper bound and a lower bound
If there is an upper bound but no lower bound or if there is a lower bound but no upper bound, the function is unbounded.
Question type: Prove that the function is bounded or unbounded, find the limit
cyclical