How to check if a function is odd. The main properties of the function: even, odd, periodicity, boundedness
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« for transportation» - 30 jobs found
(impressions: 1036 , answers: 33 )
For transportation of 37 tons of cargo for 900 km. You can use one of three carriers. Moreover, each of them has its own carrying capacity of the vehicles used. How many rubles will you have to pay for the cheapest transportation for one flight?
Job B4()(impressions: 703 , answers: 23 )
To transport 5 tons of cargo over 350 km, you can use the services of one of three carrier companies. The cost of transportation and the carrying capacity of vehicles for each carrier is indicated in the table. How many rubles will you have to pay for the cheapest transportation?
The correct answer has not yet been determined
Job B4()(impressions: 705 , answers: 22 )
To transport 6 tons of cargo for 250 km, you can use the services of one of three carrier companies. The cost of transportation and the carrying capacity of vehicles for each carrier is indicated in the table. How many rubles will you have to pay for the cheapest transportation?
The correct answer has not yet been determined
Job B4()(impressions: 697 , answers: 21 )
The correct answer has not yet been determined
Job B4()(impressions: 722 , answers: 20 )
The correct answer has not yet been determined
Job B4()(impressions: 715 , answers: 20 )
To transport 4 tons of cargo for 50 km, you can use the services of one of three carrier companies. The cost of transportation and the carrying capacity of vehicles for each carrier is indicated in the table. How many rubles will you have to pay for the cheapest transportation?
Answer: 1100
Job B4()(impressions: 720 , answers: 20 )
To transport 6 tons of cargo for 50 km, you can use the services of one of three carrier companies. The cost of transportation and the carrying capacity of vehicles for each carrier is indicated in the table. How many rubles will you have to pay for the cheapest transportation?
The correct answer has not yet been determined
Job B4()(impressions: 684 , answers: 19 )
To transport 3 tons of cargo for 50 km, you can use the services of one of three carrier companies. The cost of transportation and the carrying capacity of vehicles for each carrier is indicated in the table. How many rubles will you have to pay for the cheapest transportation?
Function zeros
The zero of the function is the value X, at which the function becomes 0, that is, f(x)=0.
Zeros are the points of intersection of the graph of the function with the axis Oh.
Function parity
A function is called even if for any X from the domain of definition, the equality f(-x) = f(x)
An even function is symmetrical about the axis OU
Odd function
A function is called odd if for any X from the domain of definition, the equality f(-x) = -f(x) is satisfied.
An odd function is symmetrical with respect to the origin.
A function that is neither even nor odd is called a general function.
Function Increment
The function f(x) is called increasing if the larger value of the argument corresponds to the larger value of the function, i.e. x 2 >x 1 → f(x 2)> f(x 1)
Decreasing function
The function f(x) is called decreasing if the larger value of the argument corresponds to the smaller value of the function, i.e. x 2 >x 1 → f(x 2)
The intervals on which the function either only decreases or only increases are called intervals of monotony. The function f(x) has 3 intervals of monotonicity:
(-∞ x 1), (x 1 , x 2), (x 3 ; +∞)
Find intervals of monotonicity using a service Intervals of increasing and decreasing function
Local maximum
Dot x 0 is called a local maximum point if for any X from a neighborhood of a point x 0 the following inequality holds: f(x 0) > f(x)
Local minimum
Dot x 0 is called a local minimum point if for any X from a neighborhood of a point x 0 the following inequality holds: f(x 0)< f(x).
Local maximum points and local minimum points are called local extremum points.
x 1 , x 2 - local extremum points.
Function Periodicity
The function f(x) is called periodic, with period T, if for any X f(x+T) = f(x) .
Constancy intervals
Intervals on which the function is either only positive or only negative are called intervals of constant sign.
f(x)>0 for x∈(x 1 , x 2)∪(x 2 , +∞), f(x)<0 при x∈(-∞,x 1)∪(x 1 , x 2)
Function continuity
The function f(x) is called continuous at the point x 0 if the limit of the function as x → x 0 is equal to the value of the function at this point, i.e. .
break points
The points at which the continuity condition is violated are called points of discontinuity of the function.
x0- breaking point.
General scheme for plotting functions
1. Find the domain of the function D(y).2. Find the intersection points of the graph of functions with the coordinate axes.
3. Investigate the function for even or odd.
4. Investigate the function for periodicity.
5. Find intervals of monotonicity and extremum points of the function.
6. Find intervals of convexity and inflection points of the function.
7. Find the asymptotes of the function.
8. Based on the results of the study, build a graph.
Example: Explore the function and build its graph: y = x 3 - 3x
8) Based on the results of the study, we will construct a graph of the function: