A function f is given. (a) Find the average rate of change

A verbal description of a function f is given. Find a formula that expresses f in function notation.Square, then subtract 5.

A verbal description of a function f is given. Find a formula that expresses f in function notation.Divide by 2, then add 9.

A formula for a function f is given. Give a verbal description of the function.f1x2 31x  102

A formula for a function f is given. Give a verbal description of the function.f1x2 16x  10

Complete the table of values for the given function.g1x2 x  4x

Complete the table of values for the given function.h1x2 3x + 2x  5

A publisher estimates that the cost C(x) of printing a run of x copies of a certain mathematics textbook is given by the function . (a) Find C(1000) and C(10,000). (b) What do your answers in part (a) represent? (c) Find C(0). What does this number represent?

Reynalda works as a salesperson in the electronics division of a department store. She earns a base weekly salary plus a commission based on the retail price of the goods she has sold. If she sells x dollars worth of goods in a week, her earnings for that week are given by the function . (a) Find E(2000) and E(15,000). (b) What do your answers in part (a) represent? (c) Find E(0). What does this number represent? (d) From the formula for E, determine what percentage Reynalda earns on the goods that she sells.

If , find , , , , , , , and .

If , find , , , , , and .

Which of the following figures are graphs of functions? Which of the functions are one-to-one?

(a) What is a one-to-one function? (b) How can you tell from the graph of a function whether it is one-to-one? (c) Suppose f is a one-to-one function with domain A and range B. How is the inverse function f 1 defined? What is the domain of f 1 ? What is the range of f 1 ? (d) If you are given a formula for f, how do you find a formula for f 1 ? (e) If you are given the graph of f, how do you find the graph of f 1 ?

Find the domain and range of the function.f1x2 1x  3

Find the domain and range of the function.f1x2 1x  3

Find the domain of the function.f1x2 7x  15

Find the domain of the function.f1x2 2x  1 2x  1

Find the domain of the function.f1x2 1x  4

Find the domain of the function.f1x2 3x  2 1x  1

Find the domain of the function.f1x2 1 x  1 x  1  1 x  2

Find the domain of the function.g1x2 2x2  5x  3 2x2  5x  3

Find the domain of the function.h1x2 14  x  2x2  1

Find the domain of the function.f1x2 23 2x  1 23 2x  2

Sketch the graph of the function.f1x2 1  2x

Sketch the graph of the function.f1x2 1 3 1x  52, 2  x  8

Sketch the graph of the function.f1t2 1  2  2t 1

Sketch the graph of the function.g1t2 t  2t 1

Sketch the graph of the function.f1x2 x2  6x  6

Sketch the graph of the function.f1x2 3  8x  2x2

Sketch the graph of the function.g1x2 1  1x

Sketch the graph of the function.g1x2  0 x 0

Sketch the graph of the function.h1x2 1 2 x3

Sketch the graph of the function.h1x2 1x  3

Sketch the graph of the function.h1x2 1 3 x

Sketch the graph of the function.H1x2 x3  3x2

Sketch the graph of the function.g1x2 1 x2

Sketch the graph of the function.G1x2 1 1x  32 2

Sketch the graph of the function.f1x2 e 1  x if x 0 1 if x  0

Sketch the graph of the function.f1x2 e 1  2x if x  0 2x  1 if x  0

Sketch the graph of the function.f1x2 e x  6 if x 2 x2 if x  2

Sketch the graph of the function.f1x2 c x if x 0 x 2 if 0  x 2 1 if x  2 f

Determine whether the equation defines y as a function.x  y 2 14

Determine whether the equation defines y as a function.3x  2y 8

Determine whether the equation defines y as a function.x 4 3  y3 27

Determine whether the equation defines y as a function.2x y 4  16

Determine which viewing rectangle produces the most appropriate graph of the function (i) 32, 24 by 32, 24 (ii) 38, 84 by 38, 84 (iii) 34, 44 by 312, 124 (iv) 3100, 1004 by 3100, 1004

Determine which viewing rectangle produces the most appropriate graph of the function . (i) 34, 44 by 34, 44 (ii) 310, 104 by 310, 104 (iii) 310, 104 by 310, 404 (iv) 3100, 1004 by 3100, 1004

Draw the graph of the function in an appropriate viewing rectangle.f1x2 x2  25x  173

Draw the graph of the function in an appropriate viewing rectangle.f1x2 1.1x3  9.6x2  1.4x  3.2

Draw the graph of the function in an appropriate viewing rectangle.f1x2 x 2x2  16

Draw the graph of the function in an appropriate viewing rectangle.f1x2 0 x1x  22 1x  42

Find, approximately, the domain of the function.f1x2 2x3  4x  1

Find, approximately, the domain of the function.f1x2 x4  x3  x2  3x  6

Draw a graph of the function f, and determine the intervals on which f is increasing and on which f is decreasing.f1x2 x 0 3  4x2

Draw a graph of the function f, and determine the intervals on which f is increasing and on which f is decreasing.

Find the average rate of change of the function between the given points.f1x2 x2  3x; x 0, x 2 f

Find the average rate of change of the function between the given points.f1x2 1 x  2 ; x 4, x 8 f

Find the average rate of change of the function between the given points.f1x2 1 x ; x 3, x 3  h f

Find the average rate of change of the function between the given points.f1x2 1x  12 2 ; x a, x a  h f

The population of a planned seaside community in Florida is given by the function , where t represents the number of years since the community was incorporated in 1985. (a) Find and . What do these values represent? (b) Find the average rate of change of P between t 10 and t 20. What does this number represent?

Ella is saving for her retirement by making regular deposits into a 401(k) plan. As her salary rises, she finds that she can deposit increasing amounts each year. Between 1995 and 2008, the annual amount (in dollars) that she deposited was given by the function , where t represents the year of the deposit measured from the start of the plan (so 1995 corresponds to t 0 and 1996 corresponds to t 1, and so on). (a) Find and . What do these values represent? (b) Assuming that her deposits continue to be modeled by the function D, in what year will she deposit $17,000? (c) Find the average rate of change of D between t 0 and t 15. What does this number represent? 61

A function f is given. (a) Find the average rate of change of f between x 0 and x 2, and the average rate of change of f between x 15 and x 50. (b) Were the two average rates of change that you found in part (a) the same? Explain why or why not. f1x2 2 x  6

A function f is given. (a) Find the average rate of change of f between x 0 and x 2, and the average rate of change of f between x 15 and x 50. (b) Were the two average rates of change that you found in part (a) the same? Explain why or why not. f1x2 8  3x 1

Suppose the graph of f is given. Describe how the graphs of the following functions can be obtained from the graph of f.(a) (b) (c) (d) (e) (f) (g) (h) y f1 y f1x2 1x2 y f1x2 y f1x2 y 1  2f1x2 y f1x  22  2 y f1x2  8 y f1x  82 f1x2

The graph of f is given. Draw the graphs of the following functions.

Determine whether f is even, odd, or neither.f1x2 x3  x7 f1x2 2x5  3x2  2 y

Determine whether the function in the figure is even, odd, or neither. (a)

Find the minimum value of the function .g1x2 2x2  4x  5

Find the maximum value of the function .f1x2 1  x  x2

A stone is thrown upward from the top of a building. Its height (in feet) above the ground after t seconds is given by What maximum height does it reach?h1t2 16t 2  48t  32

The profit P (in dollars) generated by selling x units of a certain commodity is given by What is the maximum profit, and how many units must be sold to generate it?P1x2 1500  12x  0.0004x2

Find the local maximum and minimum values of the function and the values of x at which they occur. State each answer correct to two decimal places.f1x2 3.3  1.6x  2.5x3

Find the local maximum and minimum values of the function and the values of x at which they occur. State each answer correct to two decimal places.f1x2 x2/3 16  x2 1/3

Two functions, f and g, are given. Draw graphs of f, g, and f  g on the same graphing calculator screen to illustrate the concept of graphical addition.f1x2 x  2, g1x2 x2

Two functions, f and g, are given. Draw graphs of f, g, and f  g on the same graphing calculator screen to illustrate the concept of graphical addition.f1x2 x2  1, g1x2 3  x2

If f1x2 x g1x2 4  3x 2  3x  2 and , find the following functions.(a) f  g (b) f  g (c) fg

Iff1x2 1  x andg1x2 1x  1 , find the following.f  g g  f 1f  g2 122

Find the functions , and and their domains.f1x2 3x  1, g1x2 2x  x2

Find the functions , and and their domains.f1x2 1x, g1x2 2 x  4

Findf  g  h , wheref1x2 11  x, g1x2 1  x2 f , and .h1x2 1  1x

If , find functions f, g, and h such that .f  g  h T

Determine whether the function is one-to-one.f1x2 3  x3

Determine whether the function is one-to-one.g1x2 2  2x  x2

Determine whether the function is one-to-one.h1x2 1 x4

Determine whether the function is one-to-one.r1x2 2  1x  3

Determine whether the function is one-to-one.p1x2 3.3  1.6x  2.5x3

Determine whether the function is one-to-one.q1x2 3.3  1.6x  2.5x3

Find the inverse of the function.f1x2 3x  2

Find the inverse of the function.f1x2 2x  1 3

Find the inverse of the function.f1x2 1x  12 3

Find the inverse of the function.f1x2 1  1 5 f1x2 1x  12

(a) Sketch the graph of the function (b) Use part (a) to sketch the graph of f1 . (c) Find an equation for f1 .f1x2 x 2  4 x  0

(a) Show that the function is one-to-one. (b) Sketch the graph of f. (c) Use part (b) to sketch the graph of f1 . (d) Find an equation for f1 .