Algebra

MATH 102 College Algebra Final - Fall 2019

Form B

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the slope -intercept form of the line satisfying the given conditions. 1) Through (-9,7) and (-4, 1)

6 19 16 69 6 19A)y=.xT B)y=Tx~T C)y=. -x ----

Solve.

2) 9x-3 7x-1 8+ 4 3 5

A) {-Vg} B) --} C){.4.}

16 69 D) y = TX +

1)

2)

Solve the problem. 3) How many liters of a solution that Is 10% alcohol must be mixed with 60 liters of a solution that is 3)

80% alcohol to get a solution that is 40% alcohol? A)8L B)80L C)140L D)14L

Find the domain and the range for the function. 4)

B) D: (-os, co), R: [0, co) D) 0: [0, os), R: (-co4J

4)

1

A) D:( -co,4], R[0, co) C) D:(_oo,4],R:[4,co)

Determine the intervals on which the function is increasing, decreasing, and constant. 5) 5) _________

A) Increasing on (0, ); Decreasing on (-, 0) B) Increasing on (co, 0); Decreasing on (0, _e) C) Increasing on (_co, 0); Decreasing on (0 ') D) Increasing on (-, 0); Decreasing on (_co, 0)

Determine the symmetry of the graph. 6)

A) x-axis, origin B) Origin C) x -axls D) y-axis

6)

Give the equation of the function whose graph is described.

7) The graph of y = x2 Is shifted 2 units to the right. This graph Is then vertically stretched by a factor 7) of 5 and reflected across the x -axls. Finally, the graph is shifted 7 units upward.

A) y= -5(x+ 7)2 + 2 B) y= -5(x - 2)2_i

C)y= -5(x-2)2+7 . D)y= -5(x -f-2)2+7

The graph is a translation of y .ji Find the equation that defines the function. 8)

A)y=../+4 B)y=J+4 C)y=.J

Solve the equation. 9) I8x + 3j + 4 = 12

A)JQ} B){*..J} C){.fJ}

Solve the inequality. Write your answer in interval notation. 10)17 - xl 5

A) [12, cc) B) E2, 12] C) [2,

D) y =

D) (-cc, 2] U [12, c)

8) __________

9)

10)

3

Graph the function.

1l)f(x)-" lfx>O 2 ifxO

A)

C) L]

Find the requested composition or operation. 12)f(x)=8x+15,g(x)=5x- 1

Find (f og)(x). A) 40x + 14 B) 40x + 74 C) 40x + 7

Write the number in simplest form, without a negative radicand. 13)/

A) I B) lOi C) -4kfi

11) ___________

12)

D) 40x + 23

13) D)4kfi

Simplify the power of i.

14) 463 14)

_______A) -i B)-1 C)i D)1

Identify the vertex of the parabola. 15) P(x) = 2x2 - 28x + 107

A) (7,0) B) (9,0) C) (9,7) D) (79) 15)

4

Solve. 16)(x -l0)2'81 16)

______

A)(1,19} B)(19) C)(-1-19) D){-71)

17)x2=12+5x 17) 5±I

__

A) (5 ± kJ5> B) (5, 12> C) { 2 D) {5 ±_.fi} Solve the inequality. Write your answer in interval notation.

18)x2 -5x+6~O 18) A) (-co,2] B) [2,3] C) [3, o) D) (_oo,2] u[3,

Solve the problem. 19) A farmer has 1200 feet of fence with which to fence a rectangular plot of land. The plot lies along a 19)

river so that only three sides need to be fenced. Estimate the largest area that can be fenced. A) 216,000 ft2 B) 180,000 ft2 C) 144,000 ft2 D) 270,000 ft2

20) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18 ft. Find 20) the length of the ladder if the length is 6 ft more than its distance from the wall.

A) 18 ft B) 24 ft C) 36 ft D) 30 ft

The function has a real zero between the two numbers given. Use your calculator to approximate the zero to the nearest hundredth.

21) y = x2 + 7.9x + 15.6025; -5 and -3 21) A) -4.25 B) -4 C) -3.999 D) -3.95

-

Find the complete quotient when P(x) is divided by the binomial following it.

22) P(x) = x4 + 625; x - 5 A)x3_5x2+25x_125+J_ B)x3+5x2+25x~125+J...

x-5 x-5

C) x3+5x2+25x+ 125 D) x3 +5x2~25x~125+ -.5

One zero of the polynomial is given. Find all remaining zeros.

23) P(x) = 7x3 + 26x2 + 22x - 4; -2

A) ---- B) -12 + -12-

7' 7 7 ,

7

D)6J -6-[ 7

,

7 14 '

14

22)

23) ________

Find all the zeros of the polynomial. 24)P(x)=X3~3X2 -5X-39 24)

A)3,2+i,2-i B)3, -3+Jã -3-'J D)3-3+21-3-21

Eplain how the graph off can be obtained from the graph of y

25) f(x) = 25) ________

A) Shift the graph of y =! to the right 2 units and upward 13 units.

B) Stretch the graph of y = vertically by a factor of 2 and shift to the left 13 units.

C) Stretch the graph of y =! vertically by a factor of 13 and shift to the left 2 units.

D) Shift the graph of y = to the left 13 units and downward 2 units.

Give the equations of any asymptotes of the type specified for the graph of the rational function. 8x+826) f(x) 3x - 7

vertical

A)x=- B)x=4 C)x=.} D)x=-+

x2 + 6x _7; blique 27)27) f(x) = o x-2

A)x=y+8 B)y=x -7 C)y=x+8 D)None

Solve the equation.

28)1~.2_= 28) ______x ________

A)-7,6 B)7,6 C)_ --j D)7,-6

Solve the rational inequality. Write your answer in interval notation.

29). --g>O 29)

A)[=4) B)[=] C)(o)

6

Solve the problem. 30) The time it takes to complete a certain Job varies Inversely as the number of people

working on that 30) ______ job. If it takes 32 hours for 11 carpenters to frame a house, then how long will it take 56

carpenters to do the same job? Round to the nearest tenth when necessary.

A) 6.3 hours B) 19.3 hours C) 40 hours D) 56 hours

1ff is one-to-one, find an equation for its inverse. 31)

______31) f(x) = x3 - 1

A) Not a one-to-one function B) f-1 (x) =

C) f-1(x) = D) f-1(x) = 1

Solve the equation. 32)

______32) 3(6 -3x),..L 27

A) (-3) B) (3) C) {.} D) (9)

33) Iog 81 =4 33)

A) (3) B) (20) C) (324) D) (85)

34) log5 x = 3 34)

A) (243> 8) (1 > C) (125> D) (8>

Write as a single log. 35) Iog x - loge y+5 loge z

35)

A) Iog xz5y B) loge .- C) Iog ..f. D) loge

Expand.

36) 10g5 .g.j 36)

A) 10g52 + 10g5p - 1 - 10g5k B) 10g52p - log5k

C) Iog2 + logp D)

10g5210g5p

1 + 10g5k 1og5k

7

Find the domain of the function. 37) f(x) = log (x + 6) 37) ______

B)(0,0) C)(1=) D)(6.)

Solve the equation. Round to the nearest thousandth. 38) 19(3-x) = 30

38) -

A) (-1.421) B) (1.845) C) (3.866) D) (1.421)

Solve the equation and express the solution in exact form. 39) _______39) Iog4 (x- 6) + 10g4 (x- 6) 1

A) (-8,8> B) (J> C) (8> D)

40) _______40) log 4x = log 3 + log (x + 4)

A) B) C) (12> D) (- 12>

8