Question

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.

Answer 1

Given:

The functions are

`f(x)=x`

`g(x)=x+8`

To find:

How the graphs of f and g are related.

Solution:

We have,

`f(x)=x`

`g(x)=x+8`

Using these functions, we get

`g(x)=f(x)+8` ...(1)

The translation is defined as

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

`a=0,b=8`

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

Therefore, the correct option is B.