91Ó°ÊÓ

Describe in words the variation shown by the given equation. \(z=\frac{k \sqrt{x}}{y^{2}}\)

Give the domain and the range of each quadratic function whose graph is described. The vertex is \((-1,-2)\) and the parabola opens up.

Solve each rational inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$\frac{x+5}{x+2}<0$$

a. Use the Leading Coefficient Test to determine the graph's end behavior. b. Find the \(x\) -intercepts. State whether the graph crosses the \(x\) -axis, or touches the \(x\) -axis and turns around, at each intercept. c. Find the \(y\) -intercept. d. Determine whether the graph has \(y\) -axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly. $$f(x)=-2 x^{4}+4 x^{3}$$

Write an equation in standard form of the parabola that has the same shape as the graph of \(f(x)=2 x^{2},\) but with the given point as the vertex. $$(-8,-6)$$

In a hurricane, the wind pressure varies directly as the square of the wind velocity. If wind pressure is a measure of a hurricane's destructive capacity, what happens to this destructive power when the wind speed doubles?

Write an equation in standard form of the parabola that has the same shape as the graph of \(f(x)=3 x^{2}\) or \(g(x)=-3 x^{2},\) but with the given maximum or minimum. Write an equation in standard form of the parabola that has the same shape as the graph of \(f(x)=3 x^{2}\) or \(g(x)=-3 x^{2},\) but with the given maximum or minimum. Maximum \(=4\) at \(x=-2\)

The illumination from a light source varies inversely as the square of the distance from the light source. If you raise a lamp from 15 inches to 30 inches over your desk, what happens to the illumination?

Galileo's telescope brought about revolutionary changes in astronomy. A comparable leap in our ability to observe the universe took place as a result of the Hubble Space Telescope. The space telescope was able to see stars and galaxies whose brightness is \(\frac{1}{50}\) of the faintest objects observable using ground-based telescopes. Use the fact that the brightness of a point source, such as a star, varies inversely as the square of its distance from an observer to show that the space telescope was able to see about seven times farther than a groundbased telescope.

In your own words, state the Division Algorithm.