91Ó°ÊÓ

For the following exercises, evaluate the function \(f\) at the values \(f(-2), f(-1), f(0), f(1),\) and \(f(2)\) $$f(x)=3^{x}$$

For the following exercises, evaluate the expressions, given functions \(f, g,\) and \(h :\) $$\cdot f(x)=3 x-2$$ $$\cdot g(x)=5-x^{2}$$ $$\cdot h(x)=-2 x^{2}+3 x-1$$ $$3 f(1)-4 g(-2)$$

For the following exercises, evaluate the expressions, given functions \(f, g,\) and \(h :\) $$\cdot f(x)=3 x-2$$ $$\cdot g(x)=5-x^{2}$$ $$\cdot h(x)=-2 x^{2}+3 x-1$$ $$f\left(\frac{7}{3}\right)-h(-2)$$

For the following exercises, graph \(y=x^{2}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. $$[-100,100]$$

For the following exercises, graph \(y=x^{3}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. $$[-10,10]$$

For the following exercises, graph \(y=\sqrt[3]{x}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. $$[-1,000,000,1,000,000]$$

The number of cubic yards of dirt, \(D,\) needed to cover a garden with area \(a\) square feet is given by \(D=g(a) .\) a. A garden with area 500 \(\mathrm{ft}^{2}\) requires 50 \(\mathrm{yd}^{3}\) of dirt. Express this information in terms of the function \(g .\) b. Explain the meaning of the statement \(g(100)=1\)

Let \(f(t)\) be the number of ducks in a lake \(t\) years after 1990 . Explain the meaning of each statement: a. \(f(5)=30\) b. \(f(10)=40\)

Let \(h(t)\) be the height above ground, in feet, of a rocket \(t\) seconds after launching. Explain the meaning of each statement: a. \(h(1)=200\) b. \(h(2)=350\)

Show that the function \(f(x)=3(x-5)^{2}+7\) is not one-to-one.