Question

In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = x - 16?

Answer 1

Answer: Option C.

Explanation:

The equation of the line in slope-intercept form is:

`y=mx+b`

Where the slope is "m" and the intersection of the line with the y-axis is "b".

Given the function f(x) in the form
`f(x)=x`, you can identify that:

`m=1\\b=0`

This means that the line passes through the origin (0,0)

And from the function g(x) in the form
`g(x)=x-16`, , you can identify that:

`m=1\\b=-16`

This means that the line of the function g(x) and the line of the function f(x) have the same slope, but the line of g(x) passes through the point (0,-16)

Therefore, the graph of f(x) must be shifted 16 units down to produce the graph of g(x)