91Ó°ÊÓ

Solve each problem. The weight of an object on Earth is directly proportional to the weight of that same object on the moon. A 200 -lb astronaut would weigh 32 lb on the moon. How much would a \(50-1 b\) dog weigh on the moon?

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ (g+h)(-10) $$

Solve each problem. The pressure exerted by a certain liquid at a given point is directly proportional to the depth of the point beneath the surface of the liquid. The pressure at \(30 \mathrm{~m}\) is 80 newtons. What pressure is exerted at \(50 \mathrm{~m} ?\)

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ (g-h)(10) $$

Determine whether each relation defines y as a function of \(x .\) (Solve for y first if necessary.) Give the domain. $$ y=-6 x $$

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ (g-h)(-3) $$

Solve each problem. The volume of a can of tomatoes is directly proportional to the height of the can. If the volume of the can is \(300 \mathrm{~cm}^{3}\) when its height is \(10.62 \mathrm{~cm},\) find the volume to the nearest whole number of a can with height \(15.92 \mathrm{~cm}\).

Determine whether each relation defines y as a function of \(x .\) (Solve for y first if necessary.) Give the domain. $$ y=-9 x $$

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ (g+h)(1) $$

An equation that defines y as a function \(f\) of \(x\) is given. (a) Solve for y in terms of \(x\), and write each equation using function notation \(f(x) .(b)\) Find \(f(3) .\) See Example \(6 .\) $$ \(y-3 x^{2}=2\)