함수와 그래프 전체 문제

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

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

For the following rational functions, find the intercepts and horizontal and vertical asymptotes, and sketch a graph.

$f(x)=\frac{x+4}{{x}^{2}-2x-3}$

For the following rational functions, find the intercepts and horizontal and vertical asymptotes, and sketch a graph.

$f(x)=\frac{{x}^{2}+2x-3}{{x}^{2}-4}$

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 $z=8.$

Solve the following application problem.

The distance a body falls varies directly as the square of the time it falls. If an object falls 64 feet in 2 seconds, how long will it take to fall 256 feet?