How to shift the function xe^x mathematically by one unit on the x axis?

In summary, shifting a function by one unit on the x-axis involves adding or subtracting one from the input variable (x) or the exponent of e in the mathematical representation. This causes the graph to shift horizontally by one unit. Shifting by a fraction of a unit is possible by applying the same principles. This transformation is also known as translating the graph.
  • #1
bugatti79
794
1
Hi Folks,

I have a function [tex]x {e^{-x}}[/tex] and if i shift it one unit to the right on the x-axis we have [tex](x-1) {e^{-(x-1)}}[/tex]

How do I show this mathematically?

Even consider the simple case of x^2, if we shift by 1 unit to the right it becomes (x-1)^2

What is the method mathematically?

Regards
 
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  • #2
Suppose $f(x)$ has a root at $x=a$, i.e., $f(a)=0$. Then $f(x-h)$ will have a root at $x-h=a$, or $x=a+h$. Thus, the function $f$ has been shifted $h$ units to the right.
 

FAQ: How to shift the function xe^x mathematically by one unit on the x axis?

1. How do you shift the function xe^x by one unit on the x-axis?

To shift a function by one unit on the x-axis, you need to add or subtract one from the input variable (x). In this case, you would add or subtract one from the exponent of e. This will shift the graph horizontally by one unit.

2. What is the mathematical representation of shifting a function by one unit on the x-axis?

The mathematical representation of shifting a function by one unit on the x-axis is f(x+1) or f(x-1), depending on the direction of the shift. This notation indicates that you are adding or subtracting one from the input variable (x).

3. How does shifting a function by one unit on the x-axis affect the graph?

Shifting a function by one unit on the x-axis will move the entire graph horizontally by one unit. This means that all points on the graph will be shifted one unit to the left or right, depending on the direction of the shift.

4. Can you shift a function by a fraction of a unit on the x-axis?

Yes, you can shift a function by a fraction of a unit on the x-axis. The same principles apply as shifting by a whole unit - you would add or subtract the fraction from the input variable (x) in the function.

5. Is shifting a function by one unit on the x-axis the same as translating the graph?

Yes, shifting a function by one unit on the x-axis is essentially the same as translating the graph. It is a transformation that moves the entire graph without changing its shape or orientation.

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