Section 3.1 Homework

 

1.  Describe the end behavior of each polynomial.

(a)

$y = x^3–6x^2+2x–13$

       End Behavior : y

$\to$

   _____ as x

$\to$ $\infty$

                               y

$\to \_\_\_\_\_\_\_ as x \to –\infty$

 

(b)

$y = –2x^4+18x+900$

         End Behavior:  

$y \to \_\_\_\_\_\_ as x \to \infty$

                                  

$y\to \_\_\_\_\_ as x \to –\infty$

        

 

 

2.  If c is a zero of the polynomial P, then consider the following. 

(a) P(c) =

(b) x – c is a _______  of P(x)

(c) c is a (n) _____ – intercept of the graph of P.

 

 

3.  Sketch the graph of each function by transforming the graph of an appropriate function of the form y = xⁿ from the graphs below.

5.  A polynomial function is given.  P(x) =

$x\left(x^2–9\right)$

(a) Describe the end behavior of the polynomial function.

     End Behavior : 

$y \to \_\_\_\_\_ as x \to \infty$

                             

$y \to \_\_\_\_ as x \to –\infty$

 

(b) Match the polynomial function with one of the following graphs. 

 

 

6.  A polynomial function is given.  

$Q\left(x\right) = –x^2(x^2–9)$

(a) Describe the end behavior of the polynomial function.

     End Behavior :

$y \to \_\_\_\_\_ as x \to \infty$

                            

$y\to \_\_\_\_ as x \to –\infty$

(b) Match the polynomial function with one of the following graphs. 

 

S

 

7. A polynomial function is given. 

$R\left(x\right) = –x^5+4x^3–9x$

(a) Describe the end behavior of the polynomial function.

    End Behavior :

$y \to \_\_\_\_\_ as x \to \infty$

                           

$y \to \_\_\_\_ as x \to –\infty$

 

(b) Match the polynomial function with one of the following graphs. 

 

 

8.  A polynomial function is given. 

$S\left(x\right) =\frac{1}{2}{x}^6–2x^4$

(a) Describe the end behavior of the polynomial function.

End Behavior :

$y \to \_\_\_\_\_ as x \to \infty$

                           

$y \to \_\_\_\_ as x \to –\infty$

 

 

(b) Match the polynomial function with one of the following graphs. 

 

 

 

9.   Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right)=\left(x–1\right)(x+5)$

 

10. Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right) = (3–x) (x+2)$

 

 

11. Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right) = –x(x–5)(x+4)$

 

 

12.  Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior.

$P\left(x\right) = –(4x–1)(x+1)(x+5)$

 

13.   Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right) = (x+2)(x+1)(x–2)(x–3)$

 

14.  Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right) = x(x+1)(x–1)(2–x)$

 

15.   Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right) = –2x{(x–2)}^2$

 

 

16. Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right) = (x+2){(x+1)}^2(2x–3)$

 

17.  Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. 

$P\left(x\right) = –{(x+1)}^2{(x–1)}^3(x–2)$