Question

The graph below shows two polynomial functions, f(x) and g(x):

Which of the following statements is true about the graph above?

g(x) is an odd degree polynomial with a positive leading coefficient.
f(x) is an odd degree polynomial with a positive leading coefficient.
g(x) is an even degree polynomial with a negative leading coefficient.
f(x) is an even degree polynomial with a negative leading coefficient.

Answer 1

The answer is 'f(x) is an odd degree polynomial with a positive leading coefficient'.

An odd degree polynomial with a positive leading coefficient will have the graph go towards negative infinity as x goes towards negative infinity, and go towards infinity as x goes towards infinity.

An even degree polynomial with a negative leading coefficient will have the graph go towards infinity as x goes toward negative infinity, and go towards negative infinity as x goes toward infinity.

g(x) would have a a positive leading coefficient with an even degree, as the graph goes towards infinity as x goes towards either negative or positive infinity.

Answer 2

One glance at the graphs should be enuf to tell you that one (the red one) is the graph of a parabola with positive leading coeff. and that the other is the gaph of an odd function which here happens to be y = x^3, also with a pos. lead. coeff.