Exam 2: Functions and Graphs

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft Apart?

Find the indicated composition of functions. -Let f = (-2, -7), (9, 7) and g = (-7, 9), (4, -9), (6, -7) . Find

Decide whether or not the functions are inverses of each other. -f(x) = , g(x) = 2 -

Determine whether the relation is a function. -

Find the inverse of the function. -f(x) =

Solve the problem. -The function gives the approximate total earnings of a company, in millions of dollars, where x = 0 corresponds to 1996, x = 1 corresponds to 1997, and so on. This model is valid For the years from 1996 to 2000. Determine the earnings for 1998. Round to the nearest hundredth when Necessary.

Graph the following function by transforming the given graph of y = f(x). -Sketch the graph of y = -f(x).

Find the requested function value. - (x): f(x) = , g(x) = 2x + 10

Evaluate. -Find g(a + 1) when g(x) = x - 3.

Use the vertical line test to determine whether y is a function of x. -

Write the equation of the graph after the indicated transformation(s). -The graph of y = is shifted 2 units to the left. Then the graph is shifted 9 units upward.

Determine whether the function is even, odd, or neither. -f(x) = + 5x - 8

Write a formula to express the relationship. Use k as the constant of variation. -The area of an equilateral triangle varies directly as the square of the side s.

Find the constant of variation and construct the function that is expressed in each statement. -y varies directly as x: y = 28, when x = 7

Find the requested composition of functions. -Given f(x) = 6x + 11 and g(x) = 5x - 1, find x).

Find the specified domain. -For f(x) = - 16 and g(x) = 2x + 3, what is the domain of g/f?

Determine whether or not the function is one-to-one. -f(x) = + x

Evaluate. -Find f(a + 3) when f(x) = + 5.

Determine whether the relation is a function. -{(-1, -5), (2, 1), (5, -6), (7, 3), (10, 4)}

Determine whether the equation defines y as a function of x. -y = 2