Question

If the graph of y= |x| is translated so that the point (1, 1) is moved to (4,1), what is the equation of the new graph?

Answer 1

Answer:

The new equation is y= (x-3)

Step-by-step explanation: we know that   the point (1, 1) is moved to (4,1).

So, the rule of the translation is: $(x,y) -----> (x+3, y)$

that means  the translation is 3 units to the right

Answer 2

Answer:

$y=|x-3|$

Step-by-step explanation:

The parent absolute function is

$y=|x|$

The graph of y= |x| is translated so that the point (1, 1) is moved to (4,1). It means the rule of translation is

$(x,y)\rightarrow (x+3,y)$

it means the graph of y=|x| translated 3 units right. So, the new vertex of the function is (3,0).

The vertex form of an absolute function is

$y=|x-h|+k$

The new vertex of the function is (3,0). Substitute h=3 and k=0 in the above equation.

$y=|x-3|+0$

$y=|x-3|$

Therefore, the required equation is y=|x-3|.