Thread: Finding what point is guaranteed to be on the graph.

1. [solved]Finding what point is guaranteed to be on the graph.

I have several problems that look like this.
Could someone walk me through the first one:

The graph of the function y=f(x) contains the point (2,5)

What point is guaranteed to be on the graph of y=f(x+3)-5 ?

2. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by sy416
The graph of the function y=f(x) contains the point (2,5) What point is guaranteed to be on the graph of y=f(x+3)-5 ?
From the given you know that $f(2)=5$. WHY?

What value of $x$ will introduce $f(2)$ into $f(x+3)-5$?

Then what point do you have?

3. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by Plato
From the given you know that $f(2)=5$. WHY?

What value of $x$ will introduce $f(2)$ into $f(x+3)-5$?

Then what point do you have?
I don't know. It confuses me with the y's and the f(x)'s

4. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by sy416
I don't know. It confuses me with the y's and the f(x)'s
OK. Forget the y's and the f(x)'s

You can surely answer this question.
What value of $x$ will introduce $f(2)$ into $f(x+3)-5$?

5. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by Plato
OK. Forget the y's and the f(x)'s

You can surely answer this question.
What value of $x$ will introduce $f(2)$ into $f(x+3)-5$?
2?

6. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by sy416
2?
NO! f(2+3)=f(5) $\ne$ f(2). Try again!

7. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by Plato
NO! f(2+3)=f(5) $\ne$ f(2). Try again!
BUt that's the thing I don't know how to find the x value that will introduce f(2). How do I do it? I need help understanding the problem.

8. Re: Finding what point is guaranteed to be on the graph.

Wait I think I have it...

9. Re: Finding what point is guaranteed to be on the graph.

Ohh! I have to choose an x value that will bring it back to f(2) .. soo... x= -1

y= f(-1+3)-5

y= f(2) - 5

y= 5-5

y=0

(-1,0)

Thank you!

10. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by sy416
BUt that's the thing I don't know how to find the x value that will introduce f(2). How do I do it? I need help understanding the problem.
I don't think that you are ready to do this question.

If you look at the answer in the 'back-of-the-book' it would be $(-1,0)$.

11. Re: Finding what point is guaranteed to be on the graph.

Originally Posted by Plato
I don't think that you are ready to do this question.

If you look at the answer in the 'back-of-the-book' it would be $(-1,0)$.
Nah I got it (scroll up). Thanks.