Graphs of standard functions:
Some more standard curves
1) Quadratic function
2) Cubic function
3) Reciprocal function
Transformations of graph
For y = x^2 + 3 all the y points of y = x^2 have been moved up by 5 units
The graph of y = x^2 has been translated by
2) y = f(x-a) for this the transformation is
example: Consider y = x^2 and y = (x - 3)^2
For y = (x - 2)^2 all points of y = x^2 have been moved 2 units to the right.
The graph of y = x^2 has been translated by
3) y = a f(x) for this the translation is stretch in y-axis with scale factor a.
example: sketch and write the transformation for y = 2 sinx
For y = 2 sin x all the points of y = sin x have had their y coordinate multiplied by 2, this transformation is a stretch in y direction of scale factor 2
4) y = f(ax) for this the translation is stretch in x-axis with scale factor 1/a
example: Sketch y = sinx and y = sin 2x
5) y = - f(x) is a reflection in the x- axis of y = f(x)
Example: Sketch y = x^2 and y = - x^2. write its transformation.
6) y = f(-x) is a reflection in the y-axis of y = f(x)
example:
Sketch y = (-x^3) + 1 write its transformation
For y = - x^3 + 1 all the points of y = x^3 +1 have been reflected in the y - axis
Examples explained
You can also look into
https://www.youtube.com/watch?v=2S9LUinJ8-w
No comments:
Post a Comment