Exam 8: Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

The area of a rectangular region is 187 square feet. If the length and width are each increased by 5 feet, the area is increased by 165 square feet. Find the length and width of the original rectangle.

If , find .

Graph the function.

Solve the equation by completing the square.

For the following function, first sketch the graph of its associated function, . Then draw the graph using translation and/or a reflection.

Mark works forty hours a week at a clothing store. His weekly salary is $220, plus he receives a 5% commission on sales over $1,000. Given the functions f ( x ) = 0.05 x and g ( x ) = x - 1,000, which of two compositions, ( f o g )( x ) or ( g o f )( x ), represents Mark's commission?

Solve the equation.

Graph the inequality.

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Solve the inequality.

An arch of the bridge shown in the following figure is semielliptical, and the major axis is horizontal. The arch is w = 40 feet wide and h = 15 feet high. Find the height of the arch d = 5 feet from the center of the base.

The graph below represents a function. Use the horizontal line test to decide whether the function is one-to-one. Answer yes or no .

Find the vertex of the parabola and graph it.

If f ( x ) = -5 x - 7, find .

Graph the function. f ( x ) = 2 x ²

Solve a formula for the indicated variable. , for .

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Solve the inequality.

Graph the function. f ( x ) = ( x - 2)²

Determine for the pair of functions and .