Graph Transformations: Shifting a Function 5 Units to the Right

[Ry122]

Just a quick question, how do I shift this function 5 units to the right?
y=(-.001/2)*(e^(x/1)+e^(-x/1))+1500

 

[CompuChip]

Suppose you have a function $y(x)$.
What are then the following functions?

• $y(x) + a$
• $y(x) - a$
• $y(x + a)$
• $y(x - a)$

If you don't see it, try filling in something simple like a linear graph (e.g. $y(x) = x$) and plotting the functions (two points will do for these), then try to find the argument and check that it applies to any function.

 

[HallsofIvy]

In other words, Ri122, what is meant by "shift this function 5 units to the right"?

 

[Ry122]

Okay ill elaborate.
Say the stationary point of a parabola is at (5,10). If i moved the graph 5 units to the right it would become (10,10).

 

[HallsofIvy]

Okay so the parabola looks exactly the same execpt the x values are shifted by 5. If the original parabola was y= x²- 15, (so that y(5)= 5²-15= 10) and changing x gives something of the form y= ( )²- 15, what would you put in the parentheses (i.e. changing x) so that y(10)= 15? Hint: if y= (x-5)²- 15, then y(10)= 5²- 15= 10.

Now apply that idea, along with CompuChip's initial respons to your problem.