LEADING COEFFICIENT TEST WORKSHEET

Problem 1 :

Find the right-hand and left-hand behaviors of the graph of  

f(x)  =  x⁵ + 2x³ - 3x + 5

Problem 2 :

Determine the end behavior of the graph of the polynomial function below using Leading Coefficient Test. 

P(x)  =  -x³ + 5x

Problem 3 :

Determine the end behavior of the graph of the polynomial function below using Leading Coefficient Test. 

P(x)  =  2x² - 2

Problem 4 :

Determine the end behavior of the graph of the polynomial function below using Leading Coefficient Test. 

P(x)  =  -x² + 1

Solutions

Problem 1 :

Find the right-hand and left-hand behaviors of the graph of  

f(x)  =  x⁵ + 2x³ - 3x + 5 

Solution : 

Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right as shown in the figure.

Problem 2 :

Determine the end behavior of the graph of the polynomial function below using Leading Coefficient Test. 

P(x)  =  -x³ + 5x

Solution : 

Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right as shown in the figure.

Problem 3 :

Determine the end behavior of the graph of the polynomial function below using Leading Coefficient Test. 

P(x)  =  2x² - 2

Solution : 

Because the degree is even and the leading coefficient is positive, the graph rises to the left and right as shown in the figure.

Problem 4 :

Determine the end behavior of the graph of the polynomial function below using Leading Coefficient Test. 

P(x)  =  -x² + 1

Solution : 

Because the degree is even and the leading coefficient is negative, the graph falls to the left and right as shown in the figure.

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