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| - 7\\)use the graphing tool to graph the functionsclick to enlarge graphhow is the graph of g related to the graph of f?\\(\bigcirc\\) a. the graph of g is the graph of f shifted 7 units horizontally right.\\(\bigcirc\\) b. the graph of g is the graph of f shifted 7 units vertically up.\\(\bigcirc\\) c. the graph of g is the graph of f shifted 7 units horizontally left.\\(\bigcirc\\) d. the graph of g is the graph of f shifted 7 units

Explanation:

Step1: Identify parent function

$f(x) = |x|$

Step2: Analyze transformed function

$g(x) = |x| - 7 = f(x) - 7$

Step3: Match to vertical shift rule

For $g(x)=f(x)-k$, shift down $k$ units.
Here $k=7$, so shift down 7 units.

Answer:

D. The graph of g is the graph of f shifted 7 units vertically down.