91Ó°ÊÓ

Let \(f(x)=3 x-1, g(x)=x^{2}+1,\) and \(h(x)=\frac{x+1}{3} .\) Evaluate each expression. Round approximate answers to three decimal places. $$f(g(-1))$$

Write the equation of each graph after the indicated transformation\((s)\) The graph of \(y=|x|\) is reflected in the \(x\) -axis, stretched by a factor of \(3,\) then translated seven units to the right and nine units upward.

First-Class Diver The pressure exerted by water at a point below the surface varies directly with the depth. The pressure is \(4.34 \mathrm{lb} / \mathrm{in} .^{2}\) at a depth of \(10 \mathrm{ft}\). What pressure does the sperm whale (the deepest diver among the air-breathing mammals) experience when it dives 6000 ft. below the surface?

Use transformations to graph each function and state the domain and range. $$y=3|x|-200$$

Processing Oysters The time required to process a shipment of oysters varies directly with the number of pounds in the shipment and inversely with the number of workers assigned. If 3000 lb can be processed by 6 workers in 8 hr, then how long would it take 5 workers to process 4000 lb?

Use transformations to graph each function and state the domain and range. $$y=-\frac{1}{2}|x+4|$$

Determine algebraically whether the function is even, odd, or neither. Discuss the symmetry of each function. $$f(x)=x^{3}-x$$

Let \(f(x)=|x|, g(x)=x-7,\) and \(h(x)=x^{2} .\) Write each of the following functions as a composition of functions chosen from \(f, g,\) and \(h\). $$M(x)=|x-7|$$

Make a table listing ordered pairs for each function. Then sketch the graph and state the domain and range. Identify any intervals on which \(f\) is increasing, decreasing, or constant. $$f(x)=\left\\{\begin{array}{rll} 8+2 x & \text { for } & x \leq-2 \\ x^{2} & \text { for } & -2

Write a formula that expresses the diagonal \(d\) of a square as a function of the area \(A\)