Question

The graph shows the translation, g(x), of the function f(x).

What integer represents the horizontal translation of f(x) to g(x)?

Answer 1

the answer is -4

Explanation:

the function moves to the left 4 integers on the graph so its -4

Answer 2

The integer 4 represents the horizontal translation of f(x) to g(x).

Explanation:

The translation is defined as

`g(x)=f(x+a)+b` .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From the given figure it is clear that the graph of f(x) horizontally shifts 4 units to the left. So, the value of a is 4 and the value of b is 0.

The translation for given function as

`g(x)=f(x+4)+0`

Therefore, the integer 4 represents the horizontal translation of f(x) to g(x).