함수와 그래프 전체 문제

Use synthetic division to find the quotient. If the divisor is a factor, write the factored form.

$\frac{2{x}^{3}+5{x}^{2}-7x-12}{x+3}$

Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.

$f(x)=2{x}^{3}+5{x}^{2}-6x-9$

Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.

$f(x)=4{x}^{4}+8{x}^{3}+21{x}^{2}+17x+4$

Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.

$f(x)=4{x}^{4}+16{x}^{3}+13{x}^{2}-15x-18$

Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.

$f(x)={x}^{5}+6{x}^{4}+13{x}^{3}+14{x}^{2}+12x+8$

Given the following information about a polynomial function, find the function.

It has a double zero at $x=3$ and zeroes at $x=1$ and $x=-2$. Its y-intercept is $(0,12).$

Given the following information about a polynomial function, find the function.

It has a zero of multiplicity 3 at $x=\frac{1}{2}$ and another zero at $x=-3$. It contains the point $(1,8).$

Use Descartes’ Rule of Signs to determine the possible number of positive and negative solutions.

$8{x}^{3}-21{x}^{2}+6=0$

Find the slant asymptote of the rational function.

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

Find the inverse of the function.

$f(x)=\sqrt{x-2}+4$

Find the inverse of the function.

$f(x)=3{x}^{3}-4$

Find the inverse of the function.

$f(x)=\frac{2x+3}{3x-1}$

Find the unknown value.

$y$ varies inversely as the square of $x$ and when $x=3,$ $y=2.$ Find $y$ if $x=1.$

Find the unknown value.

$y$ varies jointly with $x$ and the cube root of $z.$ If when $x=2$ and $z=27,$ $y=12,$ find $y$ if $x=5$ and $z=8.$