5.2 Power functions and polynomial functions  (Page 7/19)

Explain the difference between the coefficient of a power function and its degree.

If a polynomial function is in factored form, what would be a good first step in order to determine the degree of the function?

In general, explain the end behavior of a power function with odd degree if the leading coefficient is positive.

What is the relationship between the degree of a polynomial function and the maximum number of turning points in its graph?

What can we conclude if, in general, the graph of a polynomial function exhibits the following end behavior? As $x\to -\infty ,f(x)\to -\infty$ and as $x\to \infty ,f(x)\to -\infty .$

$f(x)=x^5$

$f(x)={\left(x^2\right)}^3$

$f(x)=x-x^4$

$f(x)=\frac{x^2}{x^2-1}$

$f(x)=2x\left(x+2\right){\left(x-1\right)}^2$

$f(x)=3^{x+1}$

$-3x{}^4$

$7-2x^2$

$-2x^2-3x^5+x-6$

$x\left(4-x^2\right)(2x+1)$

$x^2{\left(2x-3\right)}^2$

$f\left(x\right)=x^4$

$f\left(x\right)=x^3$

$f\left(x\right)=-x^4$

$f\left(x\right)=-x^9$

$f(x)=-2x^4-3x^2+x-1$

$f(x)=3x^2+x-2$

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

$f(x)={(2-x)}^7$

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

$g\left(n\right)=\mathrm{-2}\left(3n-1\right)(2n+1)$

$f(x)=x^4-16$

$f(x)=x^3+27$

$f(x)=x\left(x^2-2x-8\right)$

$f(x)=(x+3)\left(4x^2-1\right)$