MATH 1314 – College Algebra – Review Exam #1 – ANSWERS

MATH 1314 ? College Algebra ? Review Exam #1 ? ANSWERS 1) (x -1)2 + ( y + 12)2 = 64

2)

3) Center: (?25, 9); Radius: 9

4) not a function; each x-value has two different y-values

5) function; each x-value has only one y-value

6) function; passes the vertical line test, each x-value has one y-value

7) not a function; fails the vertical line test, many x-values have two different y-values

8) function; each x-value has only one y-value

9) not a function; ?1 has two different y-values

{ } 10) a)

f (-3) = 1 , 5

f

(a

+ 1)

=

a2

+

1 2a

-

3

b) D = x x -2, x 2

11) a) f (-1) = 2 , f (m + 6) = m + 9 b) D = {x x -3}

12) a) D = {x - 2 x 2} or [?2, 2] b) R = {y - 2 y 0} or [?2, 0] c) f (0) = -2

13) a) D= all real numbers b) R = {y y 2} or (?, 2] c) f (-2) = 2

14) Increasing: (?, ?1); Decreasing: (?1, )

15) Increasing: (?, ?2) U (0, 1); Decreasing: (?2, 0) U (1, )

16) 3

17)

1 5

18) a) 7 b) 4 c) ?4

19) a) 3 b) 4 c) ?1

20) a) 0 b) 0 c) 7 d) 3

21) a) 2 b) ?4 c) 0

22) a) ( f - g)(x) = 3x + 1, D=all real numbers b) 8

23) a)

(

f

/

g )( x)

=

x2 + 3x x2 -1

,

D

=

{x

x -1,

x 1}

b) ?6

24) a) (g f )(9) = 12 b) ( f g)(x) = x2 + x c) (g g)(x) = x4 + 2x3 + 2x2 + x

25) f is not one-to-one and has no inverse: the y-value of 4 has two different x-values

26)

27)

28) f -1(x) = 2x + 1 4

29) f -1(x) = 3 5 x-6

30)

x

6 5 3 1

f -1(x) ?2 0

4

6

31) y = -10x + 8

32) y = - 1 x -1 2

33) y = -8

34) a) slope: ?2; x-intercept: 3; y-intercept: 6; b) f (x) = -2x + 6 ; c) 3

35) 3.25 36) f (x) = 80x + 89

37) No solution

1 38) 17

39)

-,

5 8

40)

-

2 9

,

4 9

41) a) 2; b) x > 2 OR (2, ); c) x 2 OR (?, 2]

42) a) -3 x 3 or [?3, 3]

43) a) [?5, 5] or ?5 < x < 5

b) f (-2) = -3, f (0) = -1, f (3) = 2

b) f (-2) = 2, f (0) = 3, f (3) = 6

d) not continuous

d) continuos

44) x=10; in 1990 the median income was about $34,500

45) a) W (t) = -10t + 300 b) 230 gallons

c)

c) x-intercept: 30; tank is empty after 30 minutes y-intercept: 300; tank initially contains 300 gallons

d) D = {t 0 t 30} or [0, 30]

46) 8 mph for 1.25 hours; 10 mph for 0.5 hours 47) a) f (x) = 42.5x + 524

b) Spending increased $42.5 billion per year. In 2010, spending was $524 billion. c) $779 billion 48) 78 pounds

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