Explain why the graph of y=f(x+h) is translated to the left instead of the right.

Question

I don't exactly understand this topic of translating because it's the opposite of what I was taught...sorta. What I am trying to translate is a parabola

Answer 1

Think of it as a line first.

The same is true for the parabola or any type of graph.

 

When adding to X, the function "speeds up"; that is, the values

for y =f(x) happen sooner for y=f(x+h)

 

 

Here is a concrete example.

 

  y = f(x)  = x  <--- the identity line;

 

   So the graph has ordered pairs .... (-2,-2), (-1,-1) , (0,0), (1,1), (2,2), .... etc

 

  change that to y = f(x+1) = x+1

 

   Now the ordered pairs are ... (-2,-1), (-1,0), (0,1), (1,2), (2,3)....etc

notice that the y values happen one value sooner than the original function y=f(x) = x

 

That's why the graph shifts to the left.

 

Hope that helps

Answer 2

Suggest you graph several examples, e.g, 

y = f(x - 2)²

y = f(x + 2)²