Question

let a and b be real numbers, where a \
eq b \
eq 0. which of the following functions could represent the graph on the right?

• f(x) = x(x - a)(x - b)^2
• f(x) = (x - a)(x - b)^2
• f(x) = x(x - a)^3(x - b)
• f(x) = x^2(x - a)^2(x - b)^2

Explanation:

Identify zeroes and their multiplicities from the graph

$$
LATEXBLOCK0
$$

Match zeroes to the given variables \(a\) and \(b\)

$$
LATEXBLOCK1
$$

Select the matching function form

$$ f(x) = x(x - a)(x - b)^2 $$

Answer:

• (A) \(f(x) = x (x - a)(x - b)^2\) (Correct answer)
• (B) \(f(x) = (x - a)(x - b)^2\)
• (C) \(f(x) = x(x - a)^3(x - b)\)
• (D) \(f(x) = x^2(x - a)^2(x - b)^2\)