Question

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

Explanation:

Step1: Analyze the intersection point

The two lines (representing \( f(x) \) and \( g(x) \)) intersect at \( x = 3 \). At the intersection point, the \( y \)-values (function outputs) are equal. So, when \( x = 3 \), \( f(3) = g(3) \).

Step2: Verify other options (optional)

• For \( f(6)=g(3) \): Calculate \( f(6) \) (from \( f(x) \)'s slope) and \( g(3) \). \( f(x) \) has a steeper slope, so \( f(6)

eq g(3) \).

• For \( f(3)=g(6) \): \( g(6) \) is higher than \( g(3) \), and \( f(3)=g(3) \), so not equal.
• For \( f(6)=g(6) \): Lines have different slopes, so at \( x = 6 \), outputs differ.

Answer:

\( f(3) = g(3) \) (the option with this statement)