Pre-Calculus Word Problems 2

Pre-Calculus Word Problems 2.6 Practice Name

1. A rectangle has one corner on the graph of y = 16 – x2, another at the origin, a third on the positive y-axis, and the fourth on the positive x-axis.

a. Express the area, A, of the rectangle as a function of x. b. What is the domain of A(x)? c. Graph A(x). For what value of x is A(x) largest?

2. A rectangle is inscribed in a circle of radius 2. Let P = (x, y) be the point in Quadrant I that is a vertex of the rectangle and is on the circle.

a. Express the area, A, of the rectangle as a function of x. b. Express the perimeter, P, of the rectangle as a function of x. c. Graph A(x). For what value of x is A(x) the largest? d. Graph P(x). For what value of x is P(x) the largest?

3. A circle with radius r is inscribed in a square.

a. Express the area, A, of the square as a function of the radius of the circle. b. Express the perimeter, P, of the square as a function of the radius.

4. A semicircle with radius r is inscribed in a rectangle, so that the diameter of the semicircle is the length of the rectangle.

a. Express the area, A, of the rectangle as a function of the radius of the semicircle. b. Express the perimeter, P, of the rectangle as a function of the radius.

5. For the graph of the function, f(x), shown below:

a. Draw the graph of y = f(-x). b. Draw the graph of y = -f(x). c. Draw the graph of y = f(x + 2). d. Draw the graph of y = f(x) + 2. e. Draw the graph of y = 2f(x). f. Draw the graph of y = f(3x).

6. The hypotenuse of a right triangle measures 13cm. Find the lengths of the legs if their sum is 17cm.