The translation is given by option (C)3 units left ,1 unit down.
A translation occurs when you a graph is moved either horizontally or vertically. That is to say, each point on the parent graph gets translated in one of four directions: left, right, up, or down. There is usually addition or subtraction involved in translation.
Let us consider the function y=|x+3|-1 which is translated from the parent function of y=|x|.
The following steps are followed for the translation of the function:
- There is an horizontal shift to the left of the parent function about 3 units .
- There is a vertical shift downwards of 1 unit.
The translation can be seen in the attached graphical representation of the two functions.
The blue line represents the translated function while the red line represents the parent function.
Therefore the translation required for the function y=|x+3|-1 from y=|x| is 3 units left and one unit down .
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