Final answer:
To find the correct function that represents f(x), we need to consider the zeros or roots of the function. The correct option is b) f(x)=(x−4)(x)(x−1.5).
Step-by-step explanation:
To find the correct function that represents f(x), we need to consider the zeros or roots of the function. In this case, the function has zeros of -4, 0, and 1.5. We can use these zeros to determine the correct form of the function.
For a zero of -4, the function must have a factor of (x+4). For a zero of 0, the function must have a factor of (x). And for a zero of 1.5, the function must have a factor of (x-1.5).
Now we can look at the options: a) f(x)=(x+4)(x)(x−1.5), b) f(x)=(x−4)(x)(x−1.5), c) f(x)=(x+4)(x)(x+1.5), and d) f(x)=(x−4)(x)(x+1.5).
The correct option is b) f(x)=(x−4)(x)(x−1.5), as it includes all the necessary factors for the zeros of the function.
If a function f(x) has zeros of -4, 0, and 1.5, we can represent the function as a product of factors where each factor is zero when x is equal to one of these values. The correct function would have (x + 4) for a zero at -4, (x) or x itself for a zero at 0, and (x - 1.5) for a zero at 1.5. Hence, the correct option is:
a) f(x)=(x+4)(x)(x−1.5)
We can easily verify this by noting that each of these factors will be zero when x is equal to its respective zero:
(x + 4) will be 0 when x=-4
(x) will be 0 when x=0
(x - 1.5) will be 0 when x=1.5
None of the other options provided will yield the zeros -4, 0, and 1.5 when set to zero.