The Transformations of Graphs of Functions is Easy!

The graph of a function can be converted either by moving, stretching / compression, or reflection.

To move and stretch / compression, there are two types: horizontal and vertical.

A graph can also be expressed either during the x-axis or y-axis.

1st Vertical transformations:

A shift can also be referred to as a translation. In order to vertically translate the graph of y = f (x) by c units upwards, c add to the function. The function is now y = f (x) c.

For a downward translation of c-units whose function is y = f (x) - c. Note that in this case is c subtracted from the function y = f (x).

Generally, a vertical translation, any point (x, y) on the graph of y = f (x) is transformed to (x, Yuck) on the graph of y = f (x) c. On the other hand, each point ( x, y) on the graph of y = f (x) is transformed to (x, y - c) on the graph of y = f (x) - c.

2nd Horizontal transformations:

Horizontal translation of the function y = f (x) be processed in a different way.

When the function is shifted c units to the right, x becomes (x - c) so that the new function y = f (x - c). When the same function y = f (x) is translated c units to the left, the new function y = f (xc).

Another way to look at this is to remember that a horizontal translation means that each point (x, y) on the graph of y = f (x) is transformed to (xc, y) on the graph of y = f ( x - c). On the other hand, every point (x, y) on the graph of y = f (x) is transformed into (x - c, y) on the graph of y = f (xc).

2nd Vertical Stretching and Compression:

The next type of transformation is vertical stretch and compression.

If y = f (x) represents the graph of the original function as mentioned above, so a graph is affected by vertical stretch or compression is expressed as y = cf (x). It should be noted that when 0 1 in the function y = cf (x) is the graph "pushed" away from the x-axis (vertical stretch). X-axis is the same as the original function in both cases.

Another way to think of vertical downward and compress is that any point (x, y) on the graph of y = f (x) is transformed to (x, CY) on the graph of y = CF (x).

3rd Horizontally Stretching and Compression:

Then you must analyze horizontal stretch and compression.

If y = f (x) represents the graph of the original function as mentioned above, so a graph is affected by a horizontal stretch or compression is expressed as y = f (cx). It should be noted that when 0 1 in the function y = f (cx), the graph is "pulled" against the y-axis (horizontally downward). Y-axis is the same as the original function in both cases.

Moreover, shrinking horizontally and compressing means that each point (x, y) on the graph of y = f (x) is transformed to (x / c, y) on the graph of y = f (cx).

4th Reflection:

The last type of transformation to look at is the reflection. It is fairly straightforward to understand!

Since the original graph of y = f (x) is reflected across the x-axis, the function of the reflected graph becomes y =- f (x). On the other hand, when the same function is reflected in the y-axis function of the reflected graph y = f (-x). That's it!

Remember that the changes mentioned above can be combined within the same function, so that a graph can be moved, stretched, and reflective!