Question

which statement is true regarding the functions on the graph?
\\( f(6) = g(3) \\)
\\( f(3) = g(3) \\)
\\( f(3) = g(6) \\)
\\( f(6) = g(6) \\)

Explanation:

Step1: Find f(3) from graph

Locate x=3 on f(x): $f(3)=4$

Step2: Find g(3) from graph

Locate x=3 on g(x): $g(3)=6$

Step3: Find f(6) from graph

Locate x=6 on f(x): $f(6)=12$

Step4: Find g(6) from graph

Locate x=6 on g(x): $g(6)=9$

Step5: Verify each option

• $f(6)=g(3)$: $12

eq 6$ (false)

• $f(3)=g(3)$: $4

eq 6$ (false)

• $f(3)=g(6)$: $4

eq 9$ (false)

• $f(6)=g(6)$: $12

eq 9$ (false)
*Correction: Check intersection point: at x=3, f(3)=6, g(3)=6 (read graph correctly)

Step6: Re-verify intersection

At x=3, both functions meet: $f(3)=g(3)=6$

Answer:

B. $f(3) = g(3)$