Chapter 10- Graphs of functions

Graphs of standard functions:

Some more standard curves

1) Quadratic function

2) Cubic function

3) Reciprocal function

Transformations of graph

1) y = f(x) +a, for this transformation is 

( where a is any constant)

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