Explore: Leading Coefficient Test Solutions

Leading Coefficient Test Solutions

The leading coefficient test allows you to generalize the end behavior of a polynomial function using the leading coefficient a and the degree n. 
Recall the end behavior of a graph:

State if the degree of the graph is even or odd and if a is positive or negative. Describe the end behavior of the graph.

a = positive
n = odd

$x \to - \infty, f (x) \to - \infty, and x \to + \infty, f (x) \to + \infty$

Name the degree and leading coefficient. Describe the end behavior of the equation.

$f (x) = - \frac{1}{4} x^{7} + x^{5} + \frac{2}{3}$

$x \to - \infty, f (x) \to + \infty, and x \to + \infty, f (x) \to - \infty$ because the leading coefficient is negative and the degree is odd

$a = - \frac{1}{4}, n = 7$

Describe the end behavior of the equation.

$m (x) = 2 x^{5} {(x - 1)}^{2} (x + 3)$

$5 + 2 + 1 = 8 n = 8 a = 2$

$x \to \pm \infty, f (x) \to + \infty$

Note

It may be helpful to place an exponent of 1 beside terms and expressions where an exponent is not listed.