Question

the function f (graphed below in blue) is a transformation of function g (graphed in black). what is the formula for function f in terms of g? draw (the graph is omitted here) \\( circ g(x)+2 \\) \\( circ g(x)-2 \\) \\( circ g(x + 2) \\) \\( circ g(x - 2) \\)

Explanation:

Step1: Identify curve shift direction

Observe that the blue curve (f) is shifted downward from the black curve (g). A vertical shift down by $k$ units is given by $g(x)-k$.

Step2: Determine shift magnitude

Compare corresponding points: for example, the black curve's horizontal asymptote is at $y=0$, while the blue curve's is at $y=-2$. This confirms a downward shift of 2 units.

Step3: Match to option

A downward shift of 2 units corresponds to the formula $f(x) = g(x)-2$.

Answer:

$\boldsymbol{g(x)-2}$