Solve each application of operations and composition of functions. Dime...

Solve each application of operations and composition of functions.

Dimensions of a Rectangle Suppose that the length of a rectangle is twice its width. Let x represent the width of the rectangle.

(a) Write a formula for the perimeter P of the rectangle in terms of x alone. Then use P(x) notation to describe it as a function. What type of function is this?

(b) Graph the function P found in part (a) in the window [0, 10] by [0, 100] . Locate the point for which x = 4, and explain what x represents and what y represents.

(c) On the graph of P, locate the point with x-value 4. Then sketch a rectangle satisfying the conditions described earlier, and evaluate its perimeter if its width is this x-value. Use the standard perimeter formula. How does the result compare with the y-value shown on your screen?

(d) On the graph of P, find a point with an integer y-value. Interpret the x- and y-coordinates here.