Move Function Left

[mathdad]

Given f(x) = (x + 1)^4, we move the final graph one unit to the left. This is indicated by the positive sign inside the parentheses. Sullivan does not explain why the graph is shifted left when there is a positive sign inside the parentheses. Why is this the case?

 

[Romsek]

This is a perfect example of something that you should reason through yourself rather than ask about if you want to learn anything about math.

Consider any function, f(x), at all, and see if you can determine the nature of f(x+1).

 

[MarkFL]

When I was a student, I found it somewhat counter-intuitive that adding to the \(x\)-value makes the graph of function's curve move to the left, which I naively associated with a decrease. But, I thought about it as if I am traveling a road (from left to right on a map), and my position along the road gets increased (adding that positive value). I am going to encounter certain landmarks sooner, as if the entire road has been pulled to the left.

 

[mathdad]

When I was a student, I found it somewhat counter-intuitive that adding to the \(x\)-value makes the graph of function's curve move to the left, which I naively associated with a decrease. But, I thought about it as if I am traveling a road (from left to right on a map), and my position along the road gets increased (adding that positive value). I am going to encounter certain landmarks sooner, as if the entire road has been pulled to the left.

I understand what you are saying.

 

[Harry_the_cat]

Complete the following table and you should see why there is a move to the left.

x	x^2	(x+1)^2
-1
0
1
2

 

[mathdad]

Complete the following table and you should see why there is a move to the left.

x	x^2	(x+1)^2
-1
0
1
2

Wow! Thank you for the table. I will complete it on paper.

 

[Steven G]

Consider two functions f₁(x) = x² and f₂(x) = (x + 1)²

You should make a table with three headings: y, x-values for x² and x-values for (x + 1)²

Now under the heading y put 9, 4, 1, 0, 1, 4, 9. Under x value for x² put -3, -2, -1, 0, 1, 2, 3

Make sure that you understand where those x values came from.

Now YOU figure out what goes under x value for (x + 1)².

 

[Steven G]

Lets play a game. It is called the squaring game.

Initially whatever number you give me I will square it.
If you want me to square 5, then what number will you give me?
If you want me to square -3, then what number will you give me?
If you want me to square 7, then what number will you give me?
If you want me to square -4, then what number will you give me?

Now a little change. I will square the number that is 1 more than what you give me. (for example if you say 5, I will square 6)
If you want me to square 5, then what number will you give me? ( note that if you say 5 then I will square 6 which is NOT what you want me to square!)
If you want me to square -3, then what number will you give me?
If you want me to square 7, then what number will you give me?
If you want me to square -4, then what number will you give me?

Please answer all the questions above and think about what is going on.

 

[Steven G]

I am glad that you liked what I wrote, but now can you answer the questions?

 

[mathdad]

I am glad that you liked what I wrote, but now can you answer the questions?

Ok. I want you to square 6.