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What do each of the transformations represent?
Example Solution: g(x)= 3 * (x-1) -3
Let's recall how to write each of the transformations of the graph of f(x).
| Transformations of f(x) | |
|---|---|
| Vertical Translations | Translation up k units, k>0 y=f(x)+ k |
| Translation down k units, k>0 y=f(x)- k | |
| Horizontal Translations | Translation right h units, h>0 y=f(x- h) |
| Translation left h units, h>0 y=f(x+ h) | |
| Vertical Stretch or Compression | Vertical stretch, a>1 y= af(x) |
| Vertical compression, 0< a< 1 y= af(x) | |
| Horizontal Stretch or Compression | Horizontal stretch, 0< b<1 y=f( bx) |
| Horizontal compression, b>1 y=f( bx) | |
| Reflections | In the x-axis y=- f(x) |
| In the y-axis y=f(- x) | |
First, we choose h. Since we have a translation to the right, we need to choose a positive number for h. Let's choose 1, since it is one of the options we have. g(x)=f(x- 1)
Next, we need to choose a which is going to multiply all the outputs of f(x-1). Since this is a vertical stretch, a should be a positive number greater than 1. Let's choose 3, as it is one of the options we have. g(x)= 3* f(x-1)
Finally, we add k. Since we need a translation downwards, we have to add a negative number. Let's choose -3, as it is one of the options. g(x)=3* f(x-1)- 3
We know that f(x)=x, so let's write g(x). g(x)= 3 * (x-1) -3
