Exam 3: Functions and Their Graphs

Typical supply and demand relationships state that as the number of units for sale increases, the market price decreases. Assume that the market price, p, and the number of units for sale, x, are related by the demand equation: p = 1,600 - x Assume that the cost, C(x), of producing x items is governed by the equation C(x) = 1,000 + 70x and the revenue, R(x), generated by selling x units is governed by R(x) = 400x a. Write the cost as a function of price p. b. Write the revenue as a function of price p. c. Write the profit as a function of price p.

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1 atm. If the container changes to a volume of 2 mL, what is the resulting pressure?

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight). F = kxwhere F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).A force of 429 N will stretch the spring 33 cm. How much force to the nearest Newtons is required to stretch the spring 72 cm?

A student work at Target making $12.90 per hour and the weekly number of hours worked per week, x, varies. If Target withholds 16% of his earnings for taxes and Social Security, write a function, E(x), that expresses the student's take-home pay each week. Find the inverse function, (x). What does the inverse function tell you?

Given the graph of a one-to-one function: plot its inverse.

Given the functions ,find (f - g)(x).

Write an equation that describes the variation. Use k as the constant of variation. V varies is directly proportional to both and . V = 32 when x = 1 and t = 4.

State (a) the domain, (b) the range, and (c) the x-intervals where the function is increasing, decreasing, and constant. Find the values of f (0) and f (1).

Given the function ,find (f ? g)

Write the function that results from shifting y = + 7 to the left 2 and reflecting about the x-axis.

Write an equation that describes the variation. F is inversely proportional to both ? and L. F = when ? = 7?m and L = 200 km.

Levi's makes jeans in a variety of price ranges for juniors. The Flare 519 jeans sell for about $19, whereas the 646 Vintage Flare jeans sell for $150. The demand for Levi's jeans is inversely proportional to the price. If 200,000 pairs of the Flare 519 jeans were bought, approximately how many of the 646 Vintage Flare were bought? Round to the nearest integer.

Determine if the relationship y = , x > 0 is a function. If it is a function, determine if it is one-to-one.

Given the functions ,find (f + g)(x).

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1.5 atm. If the temperature decreases to 325 K, what is the resulting pressure?

Use the vertical line test to determine if the graph below defines a function.

The graph of y = is reflected about the x-axis and shifted up 5. Write the resulting function.

Given the functions f (x) = and g(x) = + 10, determine the composite functions and

The graph of y = is contracted by a factor of 7. Write the resulting function.

Given the functions f (x) = 18 - 4x and g(x) = 3x + 2, find (f - g)(x).