Question

which equation could possibly represent the graphed function?

\\(f(x) = (x - 4)(x + 2)(x + 4)\\)
\\(f(x) = (x - 4)^2(x - 2)\\)
\\(f(x) = (x + 4)^2(x + 2)\\)
\\(f(x) = (x - 4)(x - 2)(x + 4)\\)

Explanation:

Identify the x-intercepts from the graph

$$ x = -4, \quad x = -2, \quad x = 4 $$

Determine the factors corresponding to the intercepts

$$ (x + 4), \quad (x + 2), \quad (x - 4) $$

Construct the polynomial function

$$ f(x) = (x - 4)(x + 2)(x + 4) $$

Answer:

• (A) \(f(x) = (x - 4)(x + 2)(x + 4)\) (Correct answer)
• (B) \(f(x) = (x - 4)^2(x - 2)\)
• (C) \(f(x) = (x + 4)^2(x + 2)\)
• (D) \(f(x) = (x - 4)(x - 2)(x + 4)\)