Answer: Height of a Balloon A balloon carrying a transmitter ascends vertically from a

Fill in the blanks. A relation that assigns to each element from a set of inputs, or ________, exactly one element in a set of outputs, or ________, is called a ________.

Fill in the blanks. For an equation that represents as a function of the set of all values taken on by the ________ variable is the domain, and the set of all values taken on by the ________ variable is the range.

Fill in the blanks. If the domain of the function is not given, then the set of values of the independent variable for which the expression is defined is called the ________ ________.

Fill in the blanks. In calculus, one of the basic definitions is that of a ________ ________, given by f _x _ h_ _ f _x_ h , h _ 0.

Testing for Functions In Exercises 58, determine whether the relation represents as a function of s

Testing for Functions In Exercises 58, determine whether the relation represents as a function of s

Testing for Functions In Exercises 58, determine whether the relation represents as a function of s

Testing for Functions In Exercises 58, determine whether the relation represents as a function of s

Testing for Functions In Exercises 9 and 10, which sets of ordered pairs represent functions from to Explain.

Testing for Functions In Exercises 9 and 10, which sets of ordered pairs represent functions from to Explain.

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Testing for Functions Represented Algebraically In Exercises 1120, determine whether the equation represents as a function of x

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 2132, evaluate (if possible) the function at each specified value of the independent variable and simplify.

Evaluating a Function In Exercises 3336, complete the table.

Evaluating a Function In Exercises 3336, complete the table.

Evaluating a Function In Exercises 3336, complete the table.

Evaluating a Function In Exercises 3336, complete the table.

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 3744, find all real values of such that f (x) = 0

Finding Values for Which In Exercises 4548, find the value(s) of for which f x  x2, gx  x  2

Finding Values for Which In Exercises 4548, find the value(s) of for which f x  x4  2x2, gx  2x2

Finding Values for Which In Exercises 4548, find the value(s) of for which f x  x2  2x  1, gx  7x  5

Finding Values for Which In Exercises 4548, find the value(s) of for which f x  x  4, gx  2  x

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Finding the Domain of a Function In Exercises 4960, find the domain of the function.

Maximum Volume An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). (a) The table shows the volumes (in cubic centimeters) of the box for various heights (in centimeters). Use the table to estimate the maximum volume. (b) Plot the points from the table in part (a). Does the relation defined by the ordered pairs represent as a function of (c) Given that is a function of write the function and determine its domain.

Maximum Profit The cost per unit in the production of an MP3 player is $60. The manufacturer charges $90 per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by $0.15 per MP3 player for each unit ordered in excess of 100 (for example, there would be a charge of $87 per MP3 player for an order size of 120). (a) The table shows the profits (in dollars) for various numbers of units ordered, Use the table to estimate the maximum profit. (b) Plot the points from the table in part (a). Does the relation defined by the ordered pairs represent as a function of (c) Given that is a function of write the function and determine its domain. (Note: where R is revenue and C is cost.)

Geometry Write the area of a square as a function of its perimeter

Geometry Write the area of a circle as a function of its circumference

Path of a Ball The height (in feet) of a baseball thrown by a child is where is the horizontal distance (in feet) from where the ball was thrown. Will the ball fly over the head of another child 30 feet away trying to catch the ball? (Assume that the child who is trying to catch the ball holds a baseball glove at a height of 5 feet.)

Postal Regulations A rectangular package to be sent by the U.S. Postal Service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches (see figure). (a) Write the volume of the package as a function of What is the domain of the function? (b) Use a graphing utility to graph the function. Be sure to use an appropriate window setting. (c) What dimensions will maximize the volume of the package? Explain your answer.

Geometry A right triangle is formed in the first quadrant by the - and -axes and a line through the point (see figure). Write the area of the triangle as a function of and determine the domain of the function. Figure for 67 Figure for 68

Geometry A rectangle is bounded by the -axis and the semicircle (see figure). Write the area of the rectangle as a function of and graphically determine the domain of the function.

Prescription Drugs The percents of prescriptions filled with generic drugs in the United States from 2004 through 2010 (see figure) can be approximated by the model where represents the year, with corresponding to 2004. Use this model to find the percent of prescriptions filled with generic drugs in each year from 2004 through 2010. (Source: National Association of Chain Drug Stores)

Median Sale Price The median sale prices (in thousands of dollars) of an existing one-family home in the United States from 2000 through 2010 (see figure) can be approximated by the model where represents the year, with corresponding to 2000. Use this model to find the median sale price of an existing one-family home in each year from 2000 through 2010. (Source: National Association of Realtors)

Cost, Revenue, and Profit A company produces a product for which the variable cost is $12.30 per unit and the fixed costs are $98,000. The product sells for $17.98. Let be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost as a function of the number of units produced. (b) Write the revenue as a function of the number of units sold. (c) Write the profit as a function of the number of units sold. (Note: )

Average Cost The inventor of a new game believes that the variable cost for producing the game is $0.95 per unit and the fixed costs are $6000. The inventor sells each game for $1.69. Let be the number of games sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost as a function of the number of games sold. (b) Write the average cost per unit as a function of

Height of a Balloon A balloon carrying a transmitter ascends vertically from a point 3000 feet from the receiving station. (a) Draw a diagram that gives a visual representation of the problem. Let represent the height of the balloon and let represent the distance between the balloon and the receiving station. (b) Write the height of the balloon as a function of What is the domain of the function?

Physics The function estimates the force (in tons) of water against the face of a dam, where is the depth of the water (in feet). (a) Complete the table. What can you conclude from the table? (b) Use the table to approximate the depth at which the force against the dam is 1,000,000 tons. (c) Find the depth at which the force against the dam is 1,000,000 tons algebraically.

Transportation For groups of 80 or more people, a charter bus company determines the rate per person according to the formula where the rate is given in dollars and is the number of people. (a) Write the revenue for the bus company as a function of (b) Use the function in part (a) to complete the table. What can you conclude?

E-Filing The table shows the numbers of tax returns (in millions) made through e-file from 2003 through 2010. Let represent the number of tax returns made through e-file in the year (Source: Internal Revenue Service) (a) Find and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let represent the number of tax returns made through e-file and let correspond to 2003. (d) Use the model found in part (c) to complete the table. (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let correspond to 2003. How does the model you found in part (c) compare with the model given by the graphing utility?

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Evaluating a Difference Quotient In Exercises 7784, find the difference quotient and simplify your answer.

Matching and Determining Constants In Exercises 8588, match the data with one of the following functions and determine the value of the constant that will make the function fit the data in the table.

Matching and Determining Constants In Exercises 8588, match the data with one of the following functions and determine the value of the constant that will make the function fit the data in the table.

Matching and Determining Constants In Exercises 8588, match the data with one of the following functions and determine the value of the constant that will make the function fit the data in the table.

Matching and Determining Constants In Exercises 8588, match the data with one of the following functions and determine the value of the constant that will make the function fit the data in the table.

True or False? In Exercises 8992, determine whether the statement is true or false. Justify your answer. Every relation is a function.

True or False? In Exercises 8992, determine whether the statement is true or false. Justify your answer. Every function is a relation.

True or False? In Exercises 8992, determine whether the statement is true or false. Justify your answer. For the function the domain is and the range is

True or False? In Exercises 8992, determine whether the statement is true or false. Justify your answer. The set of ordered pairs represents a function.

Think About It Consider and Why are the domains of and different?

Think About It Consider and Why are the domains of and different?

Think About It Given is the independent variable? Why or why not?

HOW DO YOU SEE IT? The graph represents the height of a projectile after seconds. (a) Explain why is a function of (b) Approximate the height of the projectile after 0.5 second and after 1.25 seconds. (c) Approximate the domain of (d) Is t a function of h? Explain.

(a) The sales tax on a purchased item is a function of the selling price. (b) Your score on the next algebra exam is a function of the number of hours you study the night before the exam.

(a) The amount in your savings account is a function of your salary. (b) The speed at which a free-falling baseball strikes the ground is a function of the height from which it was dropped.