Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x + 4)(x – i)(x – 2)f(x) = (x – 3)(x + 4)(x – i)(x – 2)f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2)f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

The polynomial function is f(x) = 3(x+4)(x-i)(x+2).

Step-by-step explanation:

The problem can be solved by elimination. In this case the correct answer is the first, so our search is short.

First, notice that the polynomial function given by f(x) = 3(x+4)(x-i)(x+2) has exactly three roots, in fact, those roots are -4, i and 2 as the statement of the exercise asks. Moreover, as all the factors (x+4)(x-i)(x+2) have leading coefficient 1, their product will have leading coefficient 1. Then, as 3 is multiplying x+4)(x-i)(x+2), the leading coefficient of f(x) is 3.

The other three cases do not satisfy the conditions of the exercise because of all of them have more roots than -4, i and 2.

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step-by-step explanation:

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both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph