Question

The graph below shows two polynomial functions, f(x) and g(x): 6 f(x) 5 V -3 -2 2 3 4 g(x) -4 -5 -7 Which of the following statements is true about the graph above? (4 points) Of(x) is an even degree polynomial with a negative leading coefficient. g(x) is an even degree polynomial with a negative leading coefficient. Of(x) is an odd degree polynomial with a positive leading coefficient. O g(x) is an odd degree polynomial with a positive leading coefficient.

Answer 1

The function f(x) is a parabola. We can tell it is a even degree polynomial because the axis of reflection is a vertical line (it passes through the vertex).

In this case, f(x) has a double root at (0,1), but a parabola will have up to 2 roots.

It has a positive leading (quadratic in this case) coefficient, because it is concave up.

In the case of g(x), we can tell it is an odd degree polinomial, as it has a axis of reflection that is a line with slope m=-1. It is like it is reflected two times, one on an horizontal line and then on a vertical line.

The leading coefficient is positive because g(x) tends to infinity when x increases, and the leading coefficient is the one that has more weight for large values of x, so it has to be positive to have positive values of g(x).

Then, we can go through the statements.

O f(x) is an even degree polynomial with a negative leading coefficient. FALSE (the leading coefficient is positive)

O g(x) is an even degree polynomial with a negative leading coefficient. FALSE (it is an odd degree polynomial)

O f(x) is an odd degree polynomial with a positive leading coefficient. FALSE (it is an even degree polynomial).

O g(x) is an odd degree polynomial with a positive leading coefficient.​ TRUE