5.3 Graphs of polynomial functions  (Page 9/13)

$f(x)=x^5-2x,$ between $x=1$ and $x=2.$

$f(x)=-x^4+4,$ between $x=1$ and $x=3$ .

$f(x)=\mathrm{-2}{x}^3-x,$ between $x=\mathrm{–1}$ and $x=1.$

$f(x)=x^3-100x+2,$ between $x=0.01$ and $x=0.1$

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

$f(x)=x^2{\left(2x+3\right)}^5{\left(x-4\right)}^2$

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

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

$f(x)={\left(2x+1\right)}^3\left(9x^2-6x+1\right)$

$f(x)={\left(3x+2\right)}^5\left(x^2-10x+25\right)$

$f(x)=x\left(4x^2-12x+9\right)\left(x^2+8x+16\right)$

$f(x)=x^6-x^5-2x^4$

$f(x)=3x^4+6x^3+3x^2$

$f(x)=4x^5-12x^4+9x^3$

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

$f(x)=4x^4\left(9x^4-12x^3+4x^2\right)$

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

$g\left(x\right)=\left(x+4\right){\left(x-1\right)}^2$

$h\left(x\right)={\left(x-1\right)}^3{\left(x+3\right)}^2$

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

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

$n\left(x\right)=-3x\left(x+2\right)(x-4)$

Degree 3. Zeros at $x=\mathrm{–2,}$ $x=\mathrm{1,}$ and $x=3.$ y -intercept at $(0,\mathrm{–4}).$

Degree 3. Zeros at $x=\text{–5,}$ $x=\mathrm{–2},$ and $x=1.$ y -intercept at $(0,6)$

Degree 5. Roots of multiplicity 2 at $x=3$ and $x=1$ , and a root of multiplicity 1 at $x=\mathrm{–3.}$ y -intercept at $(0,9)$

Degree 4. Root of multiplicity 2 at $x=\mathrm{4,}$ and a roots of multiplicity 1 at $x=1$ and $x=\mathrm{–2.}$ y -intercept at $(0,\text{–}3).$

Degree 5. Double zero at $x=1,$ and triple zero at $x=3.$ Passes through the point $(2,15).$

Degree 3. Zeros at $x=4,$ $x=3,$ and $x=2.$ y -intercept at $\left(0,\mathrm{-24}\right).$

Degree 3. Zeros at $x=\mathrm{-3},$ $x=\mathrm{-2}$ and $x=1.$ y -intercept at $(0,12).$

Degree 5. Roots of multiplicity 2 at $x=\mathrm{-3}$ and $x=2$ and a root of multiplicity 1 at $x=\mathrm{-2.}$

y -intercept at $\left(0, 4\right).$

Degree 4. Roots of multiplicity 2 at $x=\frac{1}{2}$ and roots of multiplicity 1 at $x=6$ and $x=\mathrm{-2.}$

y -intercept at $\left(\mathrm{0,}18\right).$

Double zero at $x=\mathrm{-3}$ and triple zero at $x=0.$ Passes through the point $(1,32).$

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

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

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

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

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

A rectangle has a length of 10 units and a width of 8 units. Squares of $x$ by $x$ units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of $x.$

Consider the same rectangle of the preceding problem. Squares of $2x$ by $2x$ units are cut out of each corner. Express the volume of the box as a polynomial in terms of $x.$

A square has sides of 12 units. Squares $x+1$ by $x+1$ units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a function in terms of $x.$

A cylinder has a radius of $x+2$ units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function.

A right circular cone has a radius of $3x+6$ and a height 3 units less. Express the volume of the cone as a polynomial function. The volume of a cone is $V=\frac{1}{3}\pi r^{2}h$ for radius $r$ and height $h.$