<p>On page 704 of the Blue Book, (test 2) problem number 17, the online SAT explaination states that y=f(x+2) is the graph of y=f(x) but moved to the left two. Why is this? If it is x+2, wouldn't it shift to the right? Could anyone point me in a direction or a website where I could learn this? Thank you</p>
<p>whenever you have (x + something) it always moves in opposite direction, to the left
if you have (x - something) it always moves to the right
here:
[Function</a> Transformations / Translations: Additional Rules](<a href=“http://www.purplemath.com/modules/fcntrans2.htm]Function”>What are function reflections? How do you do them? | Purplemath)
this seems pretty helpful imo</p>
<p>Its always the opposite. Plus something means to the left while minus something means to the right. Thats a pretty elementary concept.</p>
<p>kay, thanks for the help. I am still in Algebra 2 so this concept was not introduced to me yet. Thanks a lot</p>
<p>You can use reasoning to figure it out. A function means that when you plug in an X-VALUE, you get a Y-VALUE. </p>
<p>f(x+2) and f(x) BOTH STILL USE THE SAME X-VALUE. f(x+2) simply gives you the y-value for x IF IT WERE 2 UNITS GREATER. So you move right to find the y-value, and go back left (to x+0) to input the y-value.</p>
<p>For example, lets say you have the graph y=x</p>
<p>The points are (0, 0), (1, 1), and (2, 2).
f(x) when x = 0 is 0. The point is (0, 0)
f(x+2) when x = 0 is 2. The x-value is STILL 0, so the point is (0, 2). You are INPUTTING X+2 to get the y-value, and THAT Y-VALUE CORRESPONDS to x, not x+2.</p>
<p>(0, 2) is to the left of (0, 0) because the y-value is greater. Imagine the line y = x and then imagine a parallel line above it. It is to the left.</p>