MAC 1147 Exam #1 Review

Instructions: Exam #1 will consist of 19 questions plus a bonus problem. Some questions will have mult iple parts and others will not. Some questions will be multiple choice and some will be free response. For the free response questions, be sure to show as much work as possible in order to demonstrate that you know what you are doing. The point value for each question is listed after each question. The bonus problem will be worth 10 extra credit points. Attempting the bonus problem can only help you; it can't hurt you. A scientific calculator may be used but no graphing calculators or calculators on any device (cell phone, iPod, etc.) which can be used for any other purpose. The exam will be similar to this review, although the numbers and functions may be different so the steps and details (and hence the answers) may work out different. But the ideas and concepts will be the same.

-- ---

------ ------

(1) Determine whether the relation represents a ftmction. If it is a function, state the domain and range. (3 pOints)

(i)

David --- ­ - .__-- ---.--­ ----­.... Verizol1

Juan ­ - ­ _ ______ ________ Metro PCS

Michelle ­ - ----.. Sprint

Paula

G function domain: {David, J uan, Michelle, Paula} range: {Verizon, Metro PCS, Sprint}

(b) function domain: {Verizon, Metro P CS, Sprint} range: {David , Juan, Michelle, Paula}

(c) not a fu nction

(ii) Determine whether the relation represents a function. If it is a function, state the domain and range. (3 points)

Bill -- __

Carmen z:: lake -

Tonya /

(a) function

........ p bird ------- - ---....~------ .-'-­

--~ "/ cat

7'E~ dog

~ fish

domain: {Bill, Carmen, Jake, Tonya} range: {bird, cat, dog, fish}

(b) function domain: {bird, cat, dog, fish}

~range: {Bill, Carmen, Jake, Tonya}

® not a function

(iii) Determine whether the relation represents a function. If it is a function, state the domain and range. (3 points)

{(2, -4), (1, -1), (0,0), (-1, -1), (-2, -4)}

@flUlct~o~ (b) function domam. {2, 1,0, -1, - 2} domain: {-4, -1, O} range: {-4, -1, O} range: {2, 1, 0, -1, -2}

(c) not a function

(iv) Determine whether the equation x + Iyl = 5 defines y as a function of x. (3 points)

(a) Yes

~ Iy\~ S" -X - l -

If I ~ s-- X

,= s-}(

(2) Find the value of the function. (3 points each)

(i) Find f( -2) when f(x) = x:~r

(a) -~ (b) -~ @1 (d) 9

-f(-:l')":" ~ "J.')l. - :t

- ?­ - \ - \.{- 1­

-~--(

-1 _(-­-'3

(ii) Find f( -x) when f(x) = 3x2 - 2x - 1.

@ 3X2 +2X-1 (b) 3:T;2 + 2x -J-- 1

(c) -3x2 + 2x - 1 ( d) -3x2 + 2x + 1

f( - X') -; 3 (- )(Y - ). (-x, -I

-=-- 3kl. +Z)c- \

(iii) Find f(x + 1) when f(x) = ~;:. eX2~!~-7 x2+2x-7 (d) x2-7(

C )

x-3 \_ )(~H~I x+5

lx.+I) ()t ...I' ­~"L 6.+\) -~

+(~+I) -= x..t\ -+4

"l..+t~.}1 -9 \+I+-\(

(3) Find the domain of the function. (3 points each)

(i) f(x) = 9x2 + 81

(a) [3,00) (b) (3,00) (c) (-00,3)

(d) (-00, -3) U (-3,3) U (3, (0) ~(-oo, 00)

(ii) f(x) = X~~4

(a) (-00,00) (b) x=2,-2 (c) (-00,2)U(2,00)

(d) (-00, -2J U [-2,2] U [2, (0) ~ (-00, -2) U (-2,2) U (2,00)

("-~4J y"'1..-=-~ )(.. ':: t."2.. ~ fr1>blt"", fO\~-h

(iii) f(x) = V3x ­ 15

(a) (-00, 00) (b) (5,00) @ [5,00)

(d) (-00,5) (e) (-00,5]

3'K- \'5 ~O

~X ?- \5 x~s

(iv) f(x) = ";;+8

(a) (-00,00) ~(-8,00) (c) [-8,00)

(d) (-00, -8) (e) (-00, -8]

Use the following graph to answer questions 4 - 14.

( 4) Does this graph represent a function? (2 points)

e Yes (b) No

(5) What is the domain and range of the graph? (2 points)

(a) domain: (-6, 6Xb) range: (-4,4)

domain: [-6, 6](c) domain: (-4, 4@ range: [-4,4] range: (-6,6)

domain: [-4,4] range: [-6,6]

(6) What is (are) the x-intercept(s) of the graph? (2 points)

(a) (0, 0) ~ -4,0), (-2,0), (0,0), (2,0), (4,0)

(c) (0, -4), (0, -2), (0,0), (0,2), (0,4) (d) none

(7) What is the y-intercept of the graph? (2 points)

@ O,O) (b) (-4,0), (-2,0), (0,0), (2,0), (4,0)

(c) (0, -4) , (0, -2), (0,0), (0,2), (0,4) (d) none

(8) What type of symmetry does the graph have? (2 points)

(a) .x-axis (b) even function @odd function (d) no symmetry

(9) What is the value of f( -I)? (2 points)

(a) -1 (c) 6(b) ° @-6 (10) Is f (~) positive or negative? (2 points)

@ Positive (b) negative

(11) For what numbers x is f(x) > O? (2 points)

(a) (-00,00) (b) (-2,0) U (2,4) (c) [-2,0]U[2,4]

@ry-4, -2) U (0,2) (e) [-4, -2] U [0, 2J

(12) For what numbers x is f(x) sO? (2 points)

(a) (-00,00) (b) (-2, 0) U (2,4) @[-2,0] U [2,4]

(d) (-4, -2) U (0,2) (e) [-4,-2]U[0,2J

(13) On what intervals is the function increasing, decreasing, and constant? (2 points)

(a) increasing: (-4, -2) U (0,2) (b) increasing: (-4, -2) U (0,2) decreasing: (-2,0) U (2,4) decreasing: (-2,0) U (2,4) constant: none constant: x = -4, -3, -2, -1,0,1,2,3,4

~ncreasing: (-4,3) U (-1,1) U (3, 4Xd) increasing: (-3, -1) U (1,3) decreasing: (-3, -1) U (1,3) decreasing: (-4,3) U (-1 , 1) U (3,4) constant: none constant: none

(14) State whether each point is a local maximum, local minimum, or neither. (1 point each)

(i) (-4,0)

( a) local maximum (b) local minimum ® either

(ii) (-3,4)

@local maximum (b) local minimwn (c) neither

(iii) (-2,0)

(a) local maximum (b) local minimum @neither

(iv) (-1, -6)

(a) local maximum ® lOCal minimum (c) neither

(v) (0,0)

( a) local maximum (b) local minimum @neither

(vi) (1,6)

~lOCal maximum (b) local minimum (c) neither

(vii) (2,0)

(a) local maximum (b) local minimum ~neither ( viii) (3, -4)

(a) local maximum ~local minimum (c) neither

(ix) (4, 0)

(a) local maximum (b) local minimum ~neither

(15) Let f(x) be the piecewise-defined function

x2 if - 3 ~ x < 0

f (x) = 2 if x = 0 {

2x + 1 if x> 0

(i) Find f(2). (1 point)

t~IrJ l'o~l L1,,~tiOo'\

J(l')+l ~ \(.t--l ~~

(ii) Sketch the graph of f( x) . (3 points)

-10 -5 o 5

-5

-10

(iii) State the domain and range of f(x). (2 points)

1)()~V\:: [-~,Po)

~= lo} (0)

10

(16) The graph of f is given below. Use the graph of f to graph the function H (x) = - f(x + 3) + 2. Indicate what types of transformations have been done to the graph and indicate how you know. (6 points)

o

f(x)8

6

y

4

2

-3 -2 -1 o 2 3 x

10

5

- - - - - - - - - -- "­

-10 5 10

-5

-10

(17) Determine what transformations have been done to the function g(x) = Vx to get the function f (x) below. Indicate how you know. Then graph f (x). (6 pOints)

-10 -5 o 5

-5

-10

10

(18) Determine what transformations have been done to the function g(x) = Ixl to get the function f (x) below. Indicate how you know. ~n graph f (x). (6

points) ~vp~ V f(x) = -~Ixl + 2

(]I «-tlw;", rJo.A / ~ Vfj&J ®V '(-(N"(\~ ~"I,..

10t "

, ,

. ' ,,£ ,ly.)-:;l..\ 5 "

. ' , .' , "

-5

-10

(19) Let f(x) be the quadratic function given below. Answer the following questions about f(x).

f(x) = x2 - 4x

(i) Does the graph of f open up or down? How do you know? (2 points)

(ii) What is the vertex (h, k) of f? (2 points)

X-= - i = - ...:.1..::- - -'1 :: d­2A ~(l) .l

S(2) -= :2:l._~ (0)) -= 4 - ~ -:: -4

\ Iff/ttAI::: Ca,- 't) J (iii) What are the intercepts of f? (2 points)

It := O'X -'I~~'. SeA- ] =-o ,-If\ Wort : W

0= Xa. -~)C +()) ~ 0"2 - \.f U\) :::. 0- 0

0::: X(X-I.{)

[')( -1~: (O/O).1 ('-110~ (iv) What is the domain of f? (1 point)

(v) What is the range of f? (1 point)

(vi) What are the intervals of increase and decrease of f? (2 points)

il\u-&.s\j : (~I 00)

~~~\~ (- 00) d.) (vii) What does the graph of f look like? (4 points)

10

5

-10 -5

-5

-10

10

Bonus. (i) Determine whether the following function is even, odd or neither. (4 points)

~-::::-~ _r ~V-2x ~ -2X

~ ~ f(x) = -Ixl (5x4 + 3) - - \x.\ (~,>;~ .y 3) =- _ ~(-).)" - ~(-)c) _ ~ -t~X

t-)c\(S(-~)'i + 3) -- I~~ (SA.l{ -t~)

- ~ t'L)( - (~ .f2X)--I~\ CS't\'i ~3) \)(\ (SX'1 -r1\

_ _ (_ ~ +")t. \ ~ _ .. Uk) - lx.l(s~'t -(3)-)

+(-()~- ~(~) ~o f9Jd 11M0hbJ (ii) Use completing the square to rewrite t he quadratic function f(x) =

-4x2+ 8x - 8 in the form f(x) = a(x - h)2 + k. Then use this to graph the function. ( 6 points)

10

-t(x.)-= -It)c2 +8x -~ . 5 ..f-(lC):: - ~(X.l-l~)-g

+fkJ -= - ~ (i - l'(-t~ -~ +\{ -10 -5 o 10

[~'() := -lie ... -I)' -3J Vy~ -=- (\, -4\ ~s~~

vut\cJla~

-5 - -5

-10 -JO