# Graph Transform: x(-n-1) Impact

• andrey21
In summary, the function x(-n-1) would result in a graph that is a reflection across the y-axis and then shifted one unit to the right. This can be visualized by comparing the graph of y = x2 to the graph of y = (-x - 1)2.
andrey21
How would the following function impact on a graph?

x(-n-1)

Heres what I know:

x(n-1) shift graph right by 1 step
x(-n) reflect in y axis

So would the solution be reflect in y-axis and shift right by 1??

Would it be reflected in y-axis and shifted left by 1 step??

Your "x(n - 1)" notation is very unusual, especially if you're also talking about y.

If y = f(x), then the graph of y = f(x - 1) is the translation of the graph of f by one unit to the right.

The graph of y = f(-x) is the reflection across the y-axis of the graph of f.

y = f(-x - 1) = f(-(x + 1)) consists of a reflection and a translation, in that order.

Think about how y = (-x - 1)2 looks in comparison to the untransformed function f(x) = x2.

## 1. What does the "x(-n-1)" in graph transform mean?

The "x(-n-1)" in graph transform refers to the horizontal translation of a graph. It means that the graph will shift horizontally to the left by a distance of n+1 units.

## 2. How does the "x(-n-1)" impact the shape of a graph?

The "x(-n-1)" transform will not change the shape of the graph, but it will change the position of the graph on the x-axis. The overall shape and characteristics of the graph will remain the same.

## 3. Can the "x(-n-1)" transform be applied to any type of graph?

Yes, the "x(-n-1)" transform can be applied to any type of graph, including linear, quadratic, exponential, and logarithmic functions. It will have the same impact on the position of the graph regardless of its type.

## 4. Is the "x(-n-1)" transform reversible?

Yes, the "x(-n-1)" transform is reversible. If the graph is translated horizontally by n+1 units to the left, it can be reversed by translating the graph horizontally by n+1 units to the right.

## 5. How does the value of n affect the impact of the "x(-n-1)" transform?

The value of n will determine the amount of horizontal translation of the graph. A larger value of n will result in a greater horizontal shift of the graph. For example, if n=2, the graph will shift 2+1=3 units to the left.

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