Question

the graph of ( y = f(x) ) is shown, where the function ( f ) is defined by ( f(x) = ax^3 + bx^2 + cx + d ) and ( a, b, c, ) and ( d ) are constants. for how many values of ( x ) does ( f(x) = 0 )?
a) one
b) two
c) three
d) four

Explanation:

Step1: Identify roots of $f(x)=0$

The roots of $f(x)=0$ are the x-values where the graph $y=f(x)$ intersects the x-axis ($y=0$).

Step2: Count intersection points

From the graph:

1. Intersection at $x=0$
2. Intersection between $x=4$ and $x=6$
3. Intersection between $x=-2$ and $x=0$

Total of 3 intersection points.

Answer:

C) Three