Getting ready for Exam 1 - review

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1 Getting read for Eam - review For Eam, stud ALL the homework, including supplements and in class activities from sections..5 and.,.. Good Review Problems from our book: Pages 6-9: 0 all, 7 7 all (don t do e on 67, 69) Pages 7: all. Find the simplified difference quotient of f; that is, find,h 0.. = +. = +5. Find the following for each for the function: f ( ) = +. a. f () b. f (0) c. f ( ) d. f ( ) e. f ( + ) f. f ( ) +. Find the domain of each of the following functions. a. The function f ( ) = 7. b. *The function ( f g)( ) where f ( ) = and g ( ) c. The function t 7t 8 f ( t) =. t t + 6 =.. The function i is represented b the table below. Write solutions as solution sets. r j = i (r ) a. Evaluate i( 5) b. Solve i( r ) = 5. Below, several functions are defined. a( ) = + b( ) = c( ) d( ) a. Evaluate ( a + b) (). b. Evaluate ( c d ) (). c. Evaluate d. Evaluate:

2 6. The function = represents the number N of housing units(in millions) in 005 that had r rooms, where r is an integer and 9. a. Identif the dependent and independent variables. b. Evaluate N(). Provide a verbal eplanation of the meaning of N(). + = answer the following questions. a. Is the point (, 5) on the graph of f? 7. For f ( ) b. For = what is f ( )? What point is on the graph of f? c. If f ( ) =, what is? What point(s) are on the graph of f? d. What is the domain of f? e. List an zeros of f. What points are on the graph of f? f. List the -intercept, if there is one, of the graph of f. 8. Determine whether the following equations are functions. If the are not, eplain wh. Shoe size, person in the class { } a. The set of ordered pairs ( ) b. Determine if the equation = + defines as a function of. c. Determine if the equation + = defines as a function of. 9. Describe how ou would proceed to find the domain and range of a function if ou were given its graph. How would our strateg change if ou were given the equation defining the function instead of its graph? 0. How man -intercepts can the graph of a function have? How man -intercepts can the graph of a function have?. Draw the graph of a function that has the following properties then compare our graph with another group: Domain: All real numbers Range: All real numbers Intercepts: (0, -) and (, 0) Local maimum of - is at - Local minimum of -6 is at

3 . Answer each question about the function shown in Figure. a. What is the absolute minimum of the function? b. What is the absolute maimum of the function? c. What are the local minimums of the function? d. Where does the function have local maimums? e. Where does the function s absolute minimum occur? f. Where does the function s local minimum occur? g. Where is the function concave down? h. Where is the function concave up? i. Where is the function increasing? j. Where is the function decreasing? k. Where is the function constant? l. What is the range of the function? m. What is the domain of the function? n. What are the intercepts on the function? o. What are the zeros of the function? Figure. For each of the functions in figures -, decide if the function is even, odd, or neither. In each case, write a sentence that justifies our decision. Figure : f Figure : g Figure : h Figure : k. Algebraicall establish whether each of the following functions is even, odd, or neither. In each case, verif our answer using the graphing feature of our calculator. ( ) = + 8 g ( ) f = ( ) = + k ( ) h = 5

4 5. Sketch the graph of each function if > if < 0 ( a) f ( ) = ( b) f ( ) = if if 0 < if < 0 c f = d f = = 0 if > 0 ( ) ( ) ( ) ( )

5 6. The graph of a piecewise-defined function is given. Write a definition for each function a. b Suppose the -intercepts of the graph of = f ( ) are -8 and. a. What are the -intercepts of the graph of = f ( + )? b. What are the -intercepts of the graph = f ( )? c. What are the -intercepts of = f ( )? d. What are the -intercepts of = f ( )? 8. Shown on the aes is the graph of = m( ). Sketch the function on the ais. = m( ) = m() = Describe the transformations made when graphing f ( ) graph of = f ( ). based upon a

6 0. Graph onto Figure 9 the function =. Then use transformations to determine the appearance of ( ) = + and graph that function onto Figure 0. Figure 9: Figure 0:

7 transformations onto figures 7 -. Describe each transformation in the corresponding figure = f is shown in Figure 7.. Ultimatel graph = f ( ( ) ) + onto Figure after first affecting the sequential caption. The graph of ( ) Figure 7: Figure 8: Figure 9: Figure 0: Figure : Figure :

8 . Which of the functions below are one-to-one? Find their inverses. For part a c, use notation suitable for writing in a graphing calculator. a. f ( ) = + 5 b. j( ) = c. g( ) = + + d. e. - 0 h() 0 - h() 5 f.. Use the table in #d to find the following: a. h() b. h(-) c. h - () d. h - (). Use the graph of the function f below to sketch a graph of its inverse. 5. Sa a function = g() models the birth rate ears after 990. The birth rate is defined as number of births per 000 people. a. Interpret g(0) = b. Interpret g - ()=0 6. Given the functions, f ( ) = and g( ) =, find g(f()) and f(g(-))

9 7. Given functions f and g that are represented numericall in the table, evaluate the following if possible: a. f(g()) b. f(g()) c. g(f()) d. g(f()) 5 f( ) 5 0 g( ) 0-8. Find functions f and g so that f g = H, where H ( ) = ( + ) 9. Confirm that = =, are inverses b algebraicall finding the following. In addition, find the domain of each composite function. Show our work. a. b. 0. The head circumference C of a child is related to the height H of the child (both in inches) through the function: = Epress the head circumference C as a function of height H.