Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. y = f(x + 5)

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BDaMan25

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What I initially did was subtract 5 from the x value to get an answer of (-3,4), but I've seen somewhere else that said you had to something like this.... " 4 = f(2+5)" to get an answer of (7, 4).
I am currently confused on which one is the right answer. Thanks in advance.
 
BDaMan25 said:
What I initially did was subtract 5 from the x value to get an answer of (-3,4), but I've seen somewhere else that said you had to something like this.... " 4 = f(2+5)" to get an answer of (7, 4).
I am currently confused on which one is the right answer. Thanks in advance.
Click to expand...
That "somewhere" is wrong.

To check your answer, let x = -3 and see what y is: y = f(x + 5) = f(-3 + 5) = f(2) = 4. It works.

To check their answer, let x = 7 and see what y is: y = f(x + 5) = f(7 + 5) = f(12) = ???. We have no information about that, so we can't say that (7, 4) is on the graph of the new function.

Your subtraction is correct; one way to explain why is to do what was suggested in post #2: Since you know what f(2) is, and you want to know what f(x + 5) is, you are looking for a value of x such that x + 5 = 2. And that value is your -3.

To put it another way, x is being increased by 5 before going into f, so you have to decrease it by 5 to get the known result.
 
Dr.Peterson said:
That "somewhere" is wrong.

To check your answer, let x = -3 and see what y is: y = f(x + 5) = f(-3 + 5) = f(2) = 4. It works.

To check their answer, let x = 7 and see what y is: y = f(x + 5) = f(7 + 5) = f(12) = ???. We have no information about that, so we can't say that (7, 4) is on the graph of the new function.

Your subtraction is correct; one way to explain why is to do what was suggested in post #2: Since you know what f(2) is, and you want to know what f(x + 5) is, you are looking for a value of x such that x + 5 = 2. And that value is your -3.

To put it another way, x is being increased by 5 before going into f, so you have to decrease it by 5 to get the known result.
Click to expand...
Thank you, I understand now. Very nice explanation! Nice to see that I had it right the first time haha.
 
All you know is that when it comes to f(x) that f(2) is 4. That is if you have f(some expression) all you now is that if that expression happens to equal 2, then f(that expression when it equals 2) is 4. No matter how it comes for that expression to equal 2, f(of it) = 4.

Since your expression is x+5, we want x+5 to equal 2. This happens when x=-3

This is basically what Dr Peterson wrote above.
 
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