2.3 Assignment - Graphs of Polynomials

Names of all group members?

Find the end behavior of

 $f\left(x\right)=x^3-3x^2-1$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty$  and  $\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$  and  $\lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=+\infty$  

Find the end behavior of

 $f\left(x\right)=3x^7+2x^8$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty$  and  $\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$  and  $\lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=+\infty$  

Find the end behavior of the graph.

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty$  and  $\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$  and  $\lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=+\infty$  

Find all roots of

 $f\left(x\right)=3x^3+x^2-9x-3$  

•  $-\frac{1}{3},\ \pm\sqrt{3}$  

•  $\frac{1}{3},\ \pm1$  

•  $-1,\ \pm3$  

•  $\frac{1}{3},\ \pm\sqrt{3}$  

Express the equation of the graph as a product of linear factors.

• $f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x+3\right)$

• $f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x-3\right)$

• $f\left(x\right)=\left(x+1\right)\left(x+2\right)\left(x-3\right)$

• $f\left(x\right)=\left(x-1\right)\left(x-2\right)\left(x+3\right)$

Which of the following must be a factor of

 $f\left(x\right)=x^3-7x^2-60x$  

•  $x+12$  

•  $x-6$  

•  $x+6$  

•  $x-10$  

Bob solved the quartic equation

 $f\left(x\right)=0$ .  His solutions are  $x=-1,\ \frac{5}{4},\ \frac{3}{2},\ 3$ .  

Which of the following cannot be a factor of  $f\left(x\right)$ ?

•  $3x-2$  

•  $x+1$  

•  $x-3$  

•  $4x-5$  

A quadratic function crosses the x-axis at points (-2, 0) and (3, 0).


Its standard form equation is of the form
 $ax^2+bx+c$ 

What is the value of  $b$  ?

•  $-1$  

•  $1$  

•  $-6$  

•  $6$  

A cubic function f(x) has roots at  $\ \frac{1}{4},\ \pm\sqrt{2}$ 

Find its standard form equation.

•  $4x^3-x^2-8x+2$  

•  $4x^3-x^2+8x-2$  

•  $4x^3-x^2-16x+4$  

•  $4x^3-x^2+16x-4$