Based on the function f(x)=x^4-3x^2-1 and the graph of g(x) below, which of the following statements is true

Step-by-step

Graph is for G(x), and F(x)=x^4-3x^2-1, so it does not mean that graph is for x^4-3x^2-1.

At x=+/- 2,  graph of F(x) bends back up to cross the x-axis.  This can be spotted by the positive leading coefficient of +1 in x^4-3x^2-1.

1. Graph G(x) has no roots (correct, since the visible part of the graph does not cross the x-axis)

2. F(x) has four roots (correct, by the fundamental theorem of algebra,  every single variable non-zero polynomial has exact n roots, complex or real, multiplicity counted, where n=degree of polynomial, and equals four in this case).  In this particular case, there are two real and two complex roots.

3. G(x) has 3 relative maxima (false, since we see 2 relative maxima and one relative maximum from the graph G(x).)

4. as x->+inf, F(x)->+inf, as x->-inf, F(x)->-inf.

(False, since F(x) has even degree and a positive leading coefficient, F(x)-> + inf as x-> +inf or x->-inf).

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