Question

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) = |x|\\)\\(g(x) = |x| - 6\\)\\(\\)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 6 units horizontally left\\(\\)\\(\bigcirc\\) b. the graph of g is the graph of f shifted 6 units vertically down.\\(\\)\\(\bigcirc\\) c. the graph of g is the graph of f shifted 6 units horizontally right.\\(\\)\\(\bigcirc\\) d. the graph of g is the graph of f shifted 6 units vertically up

Explanation:

To determine the relationship between the graphs of \( f(x) = |x| \) and \( g(x) = |x| - 6 \), we use the rules of function transformations. For a function \( y = f(x) + k \), if \( k>0 \), the graph shifts up \( k \) units; if \( k<0 \), it shifts down \( |k| \) units. Here, \( g(x) = f(x) - 6 \), so \( k = -6 \), meaning the graph of \( g \) is the graph of \( f \) shifted 6 units vertically down.

Answer:

B. The graph of g is the graph of f shifted 6 units vertically down.