F(x) = (x+2)(x-1)(2x+3) which statements are true? (graph is pictured) select all that apply a)the end behavior of functions f(x) and g(x) are exactly the same. b)both functions have exactly three x-intercepts. c)the function f(x) is an odd degree function. d)the function g(x) has a positive leading coefficient. e)the x intercepts for g(x) are (1, 0); (2, 0) and (-3/2, 0)
B) Both functions have exactly three x-intercepts.
C) The function f(x) is an odd degree function.
E) The x intercepts for g(x) are (1, 0); (2, 0) and (-3/2, 0)
The function f is a function of degree 3 (there are 3 x-terms in the product contributing to the highest-degree term), so is of odd degree. The leading coefficient in f(x) is the product of the coefficients of x: 1·1·2 = 2, a positive number.
For a polynomial function of odd degree, the general shape of the graph will be "/" if the leading coefficient is positive, and "\" if the leading coefficient is negative. That is, end behaviors will be opposites of each other. Function f has a positive leading coefficient, so its end behavior will be (-∞, -∞) and (+∞, +∞). Function g has end behavior that is (-∞, +∞) and (+∞, -∞), so is not the same. Apparently, g(x) has a negative leading coefficient.
The graph of g(x) shows it to have 3 x-intercepts. They can be read from the graph as (-3/2, 0), (1, 0) and (2, 0). The factoring of f(x) shows it to have 3 x-intercepts, the same number. There is an x-intercept of f(x) for each factor. (The x-intercept value is the value of x that makes the factor zero.)