Algebra-2

1. Horizontal Shift

We focus on the expression (x - 1):

In this expression, x - 1 indicates a shift in the x-direction.

When we see (x - h) (where h = 1 ), it indicates a shift to the right by h units.

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

Thus, from (x - 1), we can conclude that the graph shifts right by 1 unit.

2. Vertical Reflection

Next, we look at the negative sign in front of the 5:

The negative sign indicates that the graph will be reflected across the x-axis. This means that all y-values are inverted.

So, the graph experiences a vertical reflection.

3. Vertical Stretch

Now, we examine the coefficient -5:

The absolute value ( | -5 | = 5 ) means that the graph will undergo a vertical stretch by a factor of 5.

When the coefficient is greater than 1 (as in this case, with 5), the graph is stretched; if the coefficient were between 0 and 1 (e.g., 0.5), it would lead to a vertical compression.

Thus, the graph is stretched vertically by a factor of 5.

Summary of Transformations

Combining these three points, we can summarize:

Horizontal Shift: Shifted to the right by 1 unit.

Vertical Reflection: The graph is flipped due to the negative sign.

Vertical Stretch: The graph is stretched vertically by a factor of 5.

Conclusion

The complete transformations of the function

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