A student graphed f(x)=x and g(x)=x+8 on the same coordinate grid. Which statement describes how the graphs of f and g are related? A. The graph of f is rotated about (0,1)
B. The graph of f is translated 8 units up to create the graph of g.
C. The graph of f is translated 8 units down to create the graph of g.
D. The graph of f is shifted 18 units up to create the graph of g.

Given:

The functions are

To find:

How the graphs of f and g are related.

Solution:

We have,

Using these functions, we get

                  ...(1)

The translation is defined as

               ... (2)

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.

On comparing (1) and (2), we get

It means, the graph of f is translated 8 units up to create the graph of g.

Therefore, the correct option is B.

step-by-step explanation:

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