Solution: Find an expression for the function whose graph

Let be the function whose graph is given. (a) Estimate the value of . (b) Estimate the values of such that . (c) State the domain of (d) State the range of (e) On what interval is increasing? (f) Is even, odd, or neither even nor odd? Explain.

Determine whether each curve is the graph of a function of . If it is, state the domain and range of the function. (a)

Find the domain and range of the function. Write your answer in interval notation. f x  23x  1

Find the domain and range of the function. Write your answer in interval notation. tx  s16  x4

Find the domain and range of the function. Write your answer in interval notation. y  1  sinx

Find the domain and range of the function. Write your answer in interval notation. y tan 2x

Suppose that the graph of is given. Describe how the graphs of the following functions can be obtained from the graph of

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

Use transformations to sketch the graph of the function. y  sin 2x

Use transformations to sketch the graph of the function. y  x  22

Use transformations to sketch the graph of the function. y  1  y  2  sx 1 2 x3

Use transformations to sketch the graph of the function. y  2  sx

Use transformations to sketch the graph of the function. f x 1 x 2

Use transformations to sketch the graph of the function. x  1  x 1  x2 if x  0 if x  0

Determine whether is even, odd, or neither even nor odd.

Find an expression for the function whose graph consists of the line segment from the point to the point together with the top half of the circle with center the origin and radius 1.

If and , find the functions (a) , (b) , (c) , (d) , and their domains.

Express the function as a composition of three functions.

The graph of is given. (a) Find each limit, or explain why it does not exist. (b) State the equations of the horizontal asymptotes. (c) State the equations of the vertical asymptotes. (d) At what numbers is discontinuous? Explain.

Sketch the graph of an example of a function that satis- fies all of the following conditions: , , , , , is continuous from the right at 3

Find the limit. lim xl0 cosx  sin x

Find the limit. lim xl3 x2  9 x2  2x  3

Find the limit. lim xl3 x2  9 x2  2x  3

Find the limit. lim xl1 x2  9 x2  2x  3

Find the limit. lim hl0 h  13  1 h

Find the limit. lim tl2 t 2  4 t 3  8

Find the limit. lim rl9 sr r  94

Find the limit. lim vl4 4  v 4  v 

Find the limit. lim sl16 4  ss s  16

Find the limit. lim vl2 v 2  2v  8 v 4  16

Find the limit. lim xl 1  2x  x2 1  x  2x2

Find the limit. lim xl 1  2x 2  x4 5  x  3x4

Find the limit. lim xl (sx2  4x  1  x)

Find the limit. xl1  1 x  1  1 x2  3x  2

Find the limit. lim xl0 cot 2x csc x

Find the limit. lim tl0 t 3 tan3 2t

Use graphs to discover the asymptotes of the curve. Then prove what you have discovered y  cos2x x2

Use graphs to discover the asymptotes of the curve. Then prove what you have discovered  sx2  x  1  sx 2  x

If for 2x  1  f x  x2 0  x  3 limxl1 f x

Prove that limxl0 x2 cos1x2   0

Prove the statement using the precise definition of a limit. lim x  0 xl2 14  5x  4

Prove the statement using the precise definition of a limit. lim xl0 s 3 lim x  0

Prove the statement using the precise definition of a limit. lim   xl 1 x4  0

Prove the statement using the precise definition of a limit. lim xl4 2 sx  4 lim  

Let (a) Evaluate each limit, if it exists. (i) (ii) (iii) (iv) (v) (vi) (b) Where is discontinuous? (c) Sketch the graph o

Show that each function is continuous on its domain. State the domain.

Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. x5  x 3  3x  5  0, 1, 2

Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. 2 sin x  3  2x 0, 1