To construct the schedule of difficult function, it is not obligatory to make the table of numerical values of a variable previously. It is much simpler to construct it in purely geometrical way, in the way of shifts and deformations.
Instruction
1. To construct the schedule by shifts and deformations, attentively look at function and allocate the main part which schedule will be rather easy to be drawn (according to the table of values). For example, in function at =3sin(х-П/2) the main part at =sinx and to begin creation of the schedule at =2 √ more simply with the schedule at = √ x.
2. Make the table of numerical values of a variable for the simplified function and construct the schedule in the system of coordinates. Further begin to result it in original form.
3. To receive a type function graph at =f (ha) (for example, at =cos (x + O) or at = (x-1) ^3, shift it along abscissa axis (as a rule, oh) on distance and. At the same time the line will move to the left at a0 and to the right at a0.
4. If the number is added to function, but not to an argument at =f (x) +b (for example, at =tgx +5 or at =2+ √ x), move the schedule on ordinate axis, that is ou. At b˃0 shift the schedule up on the necessary number of units, and at b˂0 – down.
5. To construct the schedule of a look at = Af (x) (for example, at =5cosx or at =6kh), the main schedule needs to be stretched or squeezed on an axis ou. At the same time each value of function will increase in And time. The schedule will contract if A1 and stretches if A1. If at the same time A0, then in addition reflect the schedule down symmetrically concerning an axis oh.
6. In case the variable x is increased by number directly under the sign of function, that is it has an appearance at =f(kх) (for example, at = √ the 5th or at =sin3x), act in the same way. That is stretch the schedule concerning an axis oh at k˂1, squeeze at k˃1. If k˂0, then reflect it concerning an axis ou across (as all values of an argument at the same time will replace the sign with opposite).
7. For the difficult function uniting several listed changes build the schedule consistently. Begin with the transformations deforming the schedule (which are narrowing or stretching), at the end carry out transfer on necessary distance. Do not erase intermediate schedules, but you draw in other color, or a dashed line, sign each of them.