الدالة مقلوب
طريق الانشاء لصورة منحنى دالة متحرك بجيوجيبرا
نص
سيوضح هذا التطبيق الصغير أساسيات الوظائف المتبادلة. سيغير شريط التمرير a بسط الخط.
يقوم شريط التمرير h بتغيير الوضع الأفقي للمنحنى. يقوم شريط التمرير k بتغيير الوضع الرأسي للمنحني. يعكس شريط التمرير sy المنحنى عبر المحور y. يعكس شريط تمرير sx المنحنى عبر المحور السيني.
صور منحنى دالة مقلوب بالانجليزي
Rational or Reciprocal Function Transformation ExerciseThe rational or reciprocal function is y = 1/x , denoted by function g.
The transformed basic function is y = 1/(x - h) + k
Note: The 'slider' feature on the x-y coordinate plane can be used to change the h, and k values
for the following exercises. To do so, place the cursor and hold it on the dot of the slider and
slide it to the desired m and b values.
To move the slider to a different location on the x-y plane, place the cursor and hold it on the line
of the slider and move it to the desired location.
Note: You can zoom in or out with the mouse.Exercise 1Perform the following rational function transformation:
Vertical shift of 3 units up.
The new function is y=1/x +3 , denoted by function f.
Set h=0 since there is no horizontal shift
Set k=3 which represents the vertical shift of 3 units up.
Observe the transformation of the rational function.Exercise 2Perform the following rational function transformation:
Vertical shift of 3 units down.
The new function is y=1/x - 3 , denoted by function f.
Set h=0 since there is no horizontal shift
Set k= - 3 which represents the vertical shift of 3 units down.
Observe the transformation of the rational function.Exercise 3Perform the following rational function transformation:
Horizontal shift of 3 units to the right.
The new function i y=1/(x - 3) , denoted by function f.
Set h=3 which represents the horizontal shift of 3 units to the right.
Set k=0 since there is not vertical shift.
Observe the transformation of the rational function.Exercise 4Perform the following rational function transformation:
Horizontal shift of 3 units to the left.
The new function is y=1/(x+3) , denoted by function f.
Set h=- 3 which represents the horizontal shift of 3 units to the left.
Set k=0 since there is not vertical shift.
Observe the transformation of the rational function.Exercise 5Perform the following rational function transformation:
Vertical shift of 3 units up plus a horizontal shift of 3 units to the right.
New function: y = 1/(x-3) +3 , denoted by function f.
Set h=3 which represents the horizontal shift of 3 units to the right.
Set k=3 which represents the vertical shift of 3 units up.
Observe the transformation of the rational function.Exercise 6Perform the following rational function transformation:
Vertical shift of 3 units down plus a horizontal shift of 3 units to the left.
New function: y = 1/(x+3) - 3 , denoted by function f.
Set h=- 3 which represents the horizontal shift of 3 units to the left.
Set k=- 3 which represents the vertical shift of 3 units down.
Observe the transformation of the rational function.Exercise 7Perform the following rational function transformation:
Vertical shift of 3 units down plus a horizontal shift of 3 units to the right.
New function: y = 1/(x - 3) - 3, denoted by function f.
Set h= 3 which represents the horizontal shift of 3 units to the right.
Set k=- 3 which represents the vertical shift of 3 units down.
Observe the transformation of the rational function.Exercise 8Perform the following rational function transformation:
Vertical shift of 3 units up plus a horizontal shift of 3 units to the left.
New function: y = 1/(x+3) + 3, denoted by function f.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the rational function.Exercise 9Perform the following rational function transformation:
Reflection over the x-axis.
New function: y = - 1/x , denoted by function f.
Place a negative in front of the entire equation.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the rational function.Exercise 10Perform the following rational function transformation:
Reflection over the y-axis.
New function: y = 1/(-x ) , denoted by function f.
Place a negative in front of the variable x.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the rational function.Exercise 11Repeat this exercise as many times as desired until concept is mastered.
Use different values of h and k