How many times that a one-to-one function crosses the horizontal line?

We want to see how many times a one-to-one function crosses the x-axis (this is equivalent to see how many values of x are mapped into y = 0).

We will see that it crosses the x-axis only one time.

A function is a relation that maps elements from one set, the domain, into elements from another set, the range. Such that each element in the domain can be mapped into only one element in the range.

Now we add the restriction that the function is one-to-one, this means that no two elements from the domain can be mapped into the same element from the range.

With this is easy to see that the one-to-one function crosses the horizontal line only once, as the value y = 0 can be assigned to only one value in the domain.

If you want to learn more, you can read:

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answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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step-by-step explanation: