3.2 Power functions and polynomial functions  (Page 8/19)

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

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

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

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

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

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

$f(x)=-x^3$

$f(x)=x^4-5x^2$

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

$f(x)=(x-1)(x-2)(3-x)$

$f(x)=\frac{x^5}{10}-x^4$

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

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

$f(x)=x(14-2x)(10-2x)$

$f(x)=x(14-2x){(10-2x)}^2$

$f(x)=x^3-16x$

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

$f(x)=x^4-81$

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

$f(x)=x^3-2x^2-15x$

$f(x)=x^3-0.01x$

The $y-$ intercept is $(0,-4).$ The $x-$ intercepts are $(-2,0),(2,0).$ Degree is 2.

End behavior: $\text{as}x\to -\infty ,f(x)\to \infty ,\text{as}x\to \infty ,f(x)\to \infty .$

The $y-$ intercept is $(0,9).$ The $x\text{-}$ intercepts are $(-3,0),(3,0).$ Degree is 2.

End behavior: $\text{as}x\to -\infty ,f(x)\to -\infty ,\text{as}x\to \infty ,f(x)\to -\infty .$

The $y-$ intercept is $(0,0).$ The $x-$ intercepts are $(0,0),(2,0).$ Degree is 3.

End behavior: $\text{as}x\to -\infty ,f(x)\to -\infty ,\text{as}x\to \infty ,f(x)\to \infty .$

The $y-$ intercept is $(0,1).$ The $x-$ intercept is $(1,0).$ Degree is 3.

End behavior: $\text{as}x\to -\infty ,f(x)\to \infty ,\text{as}x\to \infty ,f(x)\to -\infty .$

The $y-$ intercept is $(0,1).$ There is no $x-$ intercept. Degree is 4.

End behavior: $\text{as}x\to -\infty ,f(x)\to \infty ,\text{as}x\to \infty ,f(x)\to \infty .$

An oil slick is expanding as a circle. The radius of the circle is increasing at the rate of 20 meters per day. Express the area of the circle as a function of $d,$ the number of days elapsed.

A cube has an edge of 3 feet. The edge is increasing at the rate of 2 feet per minute. Express the volume of the cube as a function of $m,$ the number of minutes elapsed.

A rectangle has a length of 10 inches and a width of 6 inches. If the length is increased by $x$ inches and the width increased by twice that amount, express the area of the rectangle as a function of $x.$

An open box is to be constructed by cutting out square corners of $x-$ inch sides from a piece of cardboard 8 inches by 8 inches and then folding up the sides. Express the volume of the box as a function of $x.$

A rectangle is twice as long as it is wide. Squares of side 2 feet are cut out from each corner. Then the sides are folded up to make an open box. Express the volume of the box as a function of the width ( $x$ ).