Algebra-2

1. Horizontal Shift

We focus on the expression (x + 2):

In this expression, x + 2 indicates a shift in the x-direction.

When we see (x + h) (where h = 2), it indicates a shift to the left by h units.

Conversely, if it were (x - h), it would indicate a shift to the right by h units.

Thus, from (x + 2), we can conclude that the graph shifts left by 2 units.

2. Vertical Compression/Stretch

Next, we look at the coefficient in front of :

The value indicates that the graph will undergo a vertical compression.

When the coefficient is between 0 and 1 (as in this case, with ), it leads to a vertical compression. If the coefficient were greater than 1, it would result in a vertical stretch.

So, the graph is compressed vertically by a factor of

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