Find the properties of various functions, and the properties of functions

Constant function y=k

1.Define the domain r

2.Range 3Parity is an even function, and when k = 0 it is an odd function again.

4.Monotonicity does not increase or decrease.

Primary function y=kx+b (k≠0).

1.Define the domain r

2.Range r

3.Parity When b=0, the odd function, otherwise, the non-odd non-even.

4.Monotonicity k>0, increase; k<0, minus.

Quadratic function y=ax 2+bx+c (a≠0).

1.Define the domain r

2.Range (c-b2 (4a) when a>0, + (-c-b2 (4a)) when a<0

3.Parity b=0, even; b≠0, non-odd and non-even.

4.Monotonnia.

When a>0, (-b 2a] decreases, [-b 2a, + increases.

When a>0, (-b 2a] increases, [-b 2a, + subtracts.]

Inverse column function y=k x (k≠0).

1.Domain.

2.Range 3Parity Odd functions.

4.Monotonnia.

k>0, (-0) minus, (0, + increase.

k>0, (-0) increase, (0, + minus.)

The primary fractional function y=(cx+d) (ax+b) (abcd≠0 and c a≠d b).

This is actually the inverse proportional function generalization in , because y=c a+(d-bc a) (ax+b).

1.Domain.

2.Range 3Parity Non-parity is not parity.

4.Monotonnia.

When d-bc a>0, (-b a) decreases, (-b a, + increases.

When d-bc a>0, (-b a) increases, (-b a, + decreases.)

The checkmark function y=x+(a x),(a≠0).

1.Domain.

2.value range a>0; a<0，r

3.Parity Odd functions.

4.Monotonnia.

a>0, (-a) increases, [-a,0) decreases, (0,a] decreases, [a,+ increases.]

a<0 (- 0) increases, (0, + increases.

Exponential function y=a x (a>0,a≠1).

1.Define the domain r

2.Range r

3.Parity Non-parity is not parity.

4.Monotonnia.

01, increase. Logarithmic function y=log a x (a>0,a≠1).

1.Define the domain r

2.Range r

3.Parity Non-parity is not parity.

4.Monotonnia.

01, increase. Power function y=x a (a≠0,a n).

1.define domain a>0,r; a<0，2.Range.

a is a positive odd number, r; a is a positive even number;

a is a negative odd number,; A is a negative even number;

3.Parity.

a is an odd number, an odd function; a is an even number, even function.

4.Monotonnia.

a is a positive odd number, increasing; a is a negative odd number, (-0) minus (0, + minus.

a is a positive even number, (-0], minus, [0, + increase.

a is a negative even number, (-00, increase, (0, + minus.)

Constant function y=k

1.Define Domain: Total.

2.Range 3Parity: Even function. If k=0, it is both an odd and even function.

4.Monotonicity: None.

The primary function y=kx+b

1.Define Domain: Total.

2.Range: The number of the whole.

3.Parity: b=0, k≠0 is an odd function.

b=0, k=0 are both odd and even functions.

b≠0,k≠0 are non-odd and non-even functions.

b≠0, k=0 At this time, the function is a constant function and an even function.

4.Monotonicity: k>0 is an increment function.

k<0 is a subtractive function.

This kind of thing, 200 points is too much.

It's all available online.

i) The sum function of a power series is a continuous function over ( r , r); (ii) If the power series converges at the left (right) endpoint of the convergence interval, then its sum function is also right (left) continuous at this endpoint.

denoted f as a function of the sum of the power series over the convergence interval (r , r), then f has the reciprocal of any order on (r , r) and can be derived term by term for any order, 3denoted f is the sum function of the power series in a certain neighborhood at the point x=0, then the coefficient of the key power series has the following relationship with the derivatives of f at x=0, and it also shows that the power series has a sum function return to the tan number f at (r,r), then the power series is uniquely determined by the derivatives of f at the point x=0.

Its properties usually refer to the definition domain, value range, analytical, monotonicity, parity, periodicity, and symmetry of the function. A function represents a correspondence in which each input value corresponds to a unique output value. The standard symbol for the output value corresponding to the input value x in the function f is f(x).

Property 1: Symmetry

Number axis symmetry: The so-called number axis symmetry means that the function image is symmetrical with respect to the axes x and y.

Origin symmetry: Again, such symmetry means that the coordinates of the coordinates of the points on the function of the image symmetry with respect to the origin, on both sides of the origin, are opposite to each other.

About point symmetry: This type is quite similar to origin symmetry, except that the symmetry point is no longer limited to the origin, but any point on the coordinate axis.

Nature 2: Periodicity

The so-called periodicity means that the image of the function in a part of the region is repeated, assuming that a function f(x) is a periodic function, then there is a real number t, when x in the defined field is added or subtracted by an integer multiple of t, the y corresponding to x does not change, then it can be said that t is the period of the function, if the absolute value of t reaches the minimum, it is called the minimum period.

The properties of functions include definition domain, value range, analytical, monotonicity, parity, periodicity, and symmetry. Suppose a function f(x) is a periodic function, then there is a real number t, and when x in the defined domain is added or subtracted by an integer multiple of t, and the y corresponding to x is unchanged, then t can be said to be the period of the function. functional.

Properties include defined domains, value domains, analytic formulas, monotonicity, parity, periodicity, and symmetry. Suppose a function f(x) is a periodic function, then there is a real number t, and when x in the defined domain is added or subtracted by an integer multiple of t, and the y corresponding to x is unchanged, then t can be said to be the period of the function.

(x) is called the Gaqi Hidden Horse function, which is defined by an integral formula, and is an elementary function without luck. The gamma function has properties: (x+1)=x (x), 0)=1, (1 2)= positive integer n, there is (n+1)=n!

Expression: (a)=

x^(a-1)]*e^(-x)]dx

Applications in MATLAB.

It represents the integer order of the integer class multiplication of n in the range n-1 to 0.

The formula is: gamma(n)=(n-1)*(n-2)*2*1 For example: gamma(6)=5*4*3*2*1ans=120