Graph of functions

[Guest]

Lets say there is a function:
y = f(x) = x^2

Now if we write f(x - 1). This means we are shifting f(x) right one unit in the positive x-axis. Ok that is good.
Now if we write f(x) - 1 = y -1. This means we are shift f(x) = y downwards toward negative y-axis.

So here is my query:
Why in the case of y - 1 the graph is not shited towards positive y-axis as in case of x - 1?

[Guest]

You've confused your equations a little bit.

We start with [tex]y = f(x)[/tex], this is just some arbitrary graph.
Now we consider replacing [tex]x[/tex] with [tex]x-1[/tex] to get [tex]y = f(x-1)[/tex]. This the same graph as [tex]y=f(x)[/tex] but shifted horizontally to the right by 1.

So far so good.

Finally we consider [tex]y = f(x)-1[/tex] this can be re-written as [tex](y+1) = f(x)[/tex] and so is equivalent to replacing [tex]y[/tex] with [tex]y+1[/tex] in the equation [tex]y=f(x)[/tex]. So we should see the graph [tex]f(x)[/tex] shifted vertically up by 1.

Because the constant switched sides to combine with the [tex]y[/tex] the sign changes and so it moves the graph in the opposite direction you were expecting.

Hope this helped,

R. Baber.

[Guest]

Oops I made a small typo. When I said "vertically up" I meant "vertically down". My argument is still fine though.

Rahil