Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How can we use the graph of $y=2^x$ to sketch the graph of $y=2^{x-1}$?

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

Note that for any $x,y$ graph: $y = f(x-1)$ is just the graph $y = f(x)$ shifted over one unit to the right.

share|improve this answer
    
Why does it shift over one unit to the right instead of left? –  jaykirby Jul 3 '13 at 11:19
1  
I'll explain it like this: where you once had $f(0)$, you now have $f(0-1)=f(-1)$. That is, $f(-1)$ was shifted to the right to cover $x=0$. –  Omnomnomnom Jul 3 '13 at 11:21
    
Could you try explaining it to me without the f's..I get confused easily by that.. –  jaykirby Jul 3 '13 at 11:24
    
@omnomnomnon: What happens to the y value, it is always going to be one less isn't it? –  jaykirby Jul 3 '13 at 11:44
1  
So to explain it without all the $f$'s, let's look at $2^x$ and $2^{x-1}$ over the numbers $\{1,2,3\}$. We have: $$2^1=2;2^{1-1}=1\\ 2^2=4; 2^{2-1}=2\\ 2^3=8; 2^{3-1}=4$$ At each $x$, the second graph takes the value that was the $y$ at one to its left. The result, if you graphed this, is that $2^{x-1}$ is shifted to the right by one. Does that make sense? –  Omnomnomnom Jul 3 '13 at 14:01
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.