91Ó°ÊÓ

Write a sentence using the variation terminology of this section to describe the formula. Volume of a sphere: \(V=\frac{4}{3} \pi r^{3}\)

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope \(m\). Sketch the line. \((-5.1,1.8), \quad m=5\)

Graph the function. $$ k(x)=\left\\{\begin{array}{ll} 2 x+1, & x \leq-1 \\ 2 x^{2}-1, & -11 \end{array}\right. $$

Write a sentence using the variation terminology of this section to describe the formula. Volume of a right circular cylinder: \(V=\pi r^{2} h\)

The polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: \((5,8),(3,6),(7,6),\) (5,2) Shift: 6 units downward, 10 units to the left

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$ y=\sqrt[3]{x+1} $$

Find all real values of \(x\) such that \(f(x)=0\). $$ f(x)=x^{2}-8 x+15 $$

Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\frac{1}{x^{2}} $$

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. $$ h(x)=x^{3}-6 x^{2}+15 $$

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope \(m\). Sketch the line. \((2.3,-8.5), \quad m=-2.5\)