91Ó°ÊÓ

Draw the following intervals on the number line. $$[-1,4]$$

Graph the following equations. $$y=3$$

Factor the polynomials. $$x^{2}+8 x+15$$

If \(f(x)=x^{3}+x^{2}-x-1,\) find \(f(1), f(-1), f\left(\frac{1}{2}\right),\) and \(f(a).\)

Factor the polynomials. $$3 x^{2}+12 x+12$$

Suppose that the cost (in millions of dollars) to remove \(x\) percent of a certain pollutant is given by the cost-benefit function $$f(x)=\frac{20 x}{102-x} \text { for } 0 \leq x \leq 100.$$ (a) Find the cost to remove \(85 \%\) of the pollutant. (b) Find the cost to remove the final \(5 \%\) of the pollutant.

Compute the numbers. $$9^{1.5}$$

Compute the numbers. $$(81)^{0.75}$$

If \(f(x)=x^{2},\) find \(f(x+h)-f(x)\) and simplify.

During the first \(\frac{1}{2}\) hour, the employees of a machine shop prepare the work area for the day's work. After that, they turn out 10 precision machine parts per hour, so the output after \(t\) hours is \(f(t)\) machine parts, where \(f(t)=10\left(t-\frac{1}{2}\right)=10 t-5\) \(\frac{1}{2} \leq t \leq 8 .\) The total cost of producing \(x\) machine parts is \(C(x)\) dollars, where \(C(x)=.1 x^{2}+25 x+200.\) (a) Express the total cost as a (composite) function of \(t.\) (b) What is the cost of the first 4 hours of operation?