Question

watch the video and then solve the problem given below
click here to watch the video.
graph the given functions, f and g, in the same rectangular coordinate system. describe how the graph of g is related to the graph of f.
\\( f(x) = -4x \\)
\\( g(x) = -4x - 4 \\)
use the graphing tool to graph the functions.
how is the graph of g related to the graph of f?
\\( \bigcirc \\) a. the graph of g is the graph of f shifted 4 units horizontally right.
\\( \bigcirc \\) b. the graph of g is the graph of f shifted 4 units vertically down.
\\( \bigcirc \\) c. the graph of g is the graph of f shifted 4 units vertically up.
\\( \bigcirc \\) d. the graph of g is the graph of f shifted 4 units horizontally left.

Explanation:

Step1: Identify function forms

$f(x) = -4x$, $g(x) = -4x - 4 = f(x) - 4$

Step2: Recall vertical shift rule

For $g(x) = f(x) - k$, graph shifts down $k$ units.
Here $k=4$, so shift down 4 units.

Answer:

B. The graph of g is the graph of f shifted 4 units vertically down.