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.

Step-by-step 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)