# Uniform linear splines is my equation correct?

1. Nov 4, 2012

### SMA_01

The question as stated: Define the uniform linear splines Hk:=H0(x−k), k=−1,0,1,2,3, where

H0={x, 0≤x<1,

2−x, 1≤x<2,

0, otherwise.

For k=−1, I would get:

H−1={x+1, 1≤x<2,

1−x, 2≤x<3,

0, otherwise.

Is that correct?

Thank you.

Last edited: Nov 4, 2012
2. Nov 4, 2012

### LCKurtz

No. $H_{-1}$ would be $H_0$ translated one unit to the left. You moved it to the right.

3. Nov 4, 2012

### haruspex

H−1(x)=H0(x+1), right?
H0(x)={x+1, 0≤x<1,
2−x, 1≤x<2,
0, otherwise}​
To get H0(x+1), wouldn't you write x+1 for x everywhere in the definition of H0(x)?

4. Nov 4, 2012

### SMA_01

LCKurtz-Wouldn't I just plug in k=-1, into H_0(x-(-1))=H_0(x+1)?

5. Nov 4, 2012

### SMA_01

haruspex-

I accidently put x+1 for the first function in H0, it's supposed to be x.

Yes, I see what you mean. I thought I did that though:
H−1={x+1, 1≤x<2,

1−x, 2≤x<3,

0, otherwise.

I don't see what I'm doing wrong...

6. Nov 4, 2012

### haruspex

No, you should have got:
H0(x+1)={x+1, 0≤x+1<1,
1−x, 1≤x+1<2,​

7. Nov 4, 2012

### SMA_01

Oh okay, I see what you mean. I though I could evaluate it at the inequalities. Thanks!