Question

suppose f(x)=x^2. find the graph of f(x+2)

Answer 1

like a first step find the f(x+2) = ?

Answer 2

??

Answer 3

substitute the x+2 in place of x

than you know that f(x)=x^2 so how will be f(x+2)=?

Answer 4

im not to sure thats why im here

Answer 5

than f(x)=x^2 when substitute the (x+2) in place of x what will get ?

Answer 6

This form means to plug in x+2 for every time we see x in the function.

Answer 7

So, I first write the function without x's but leaving open parentheses in their place.

( )^2

Answer 8

Then plug in the x+2 into the parentheses. Can you try that step?

Answer 9

This problem is simply a transformation.
If you know what f(x) = x^2 looks like, then since you are asked for f(x + 2), you see that you are replacing x with x + 2.

In a function, when you replace x with x - h, you end up with a translation of h units horizontally.
In this case, f(x + 2) = f (x - (-2))
h = -2, and it is a translation of 2 units to the left.