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Functions, Logarithms, Equations

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Textbook Reading Assignment

Read the chapter section on Functions in the College Algebra textbook.

Review of Course Topics in College Algebra

For (1) through (25) : choose from (a) , (b) , (c) , (d) or (e) to answer the given problem.

(1)

Simplify the following numerical expression.

23 − ( − 4 ) ²

( − 2 ) ² − ( − 3 )

(a) 0 (b) 4.75 (c) 0.50 (d) − 2 (e) 1

(2) The volume of a rectangular solid is 1,296 cubic inches. If the height is twice the length and the width of the rectangular solid is 8 , find the length of the solid.

(a) 12 (b) 6 (c) 10 (d) 8 (e) 9

(3) Consider the solution of the following system of equations. What is the value of y in the

solution of this system? 5 x + 7 y = − 52

5 x − 5 y = − 20

(a) y = − 2 (b) y = 16 (c) y = − 6 (d) y = 3 (e) y = − 4

(4) Solve the equation for A . 3 A + 5 ( A − 2 A ) + 4 = − 8 A

(a) 1.4 (b) − 4 / 9 (c) − 2 / 3 (d) − 0.4 (e) 3 / 2

(5) Find the remainder when x ⁴ − 4 x ²+ x + 9 is divided by x + 1 .

(a) 5 (b) − 4 (c) 6 (d) 7 (e) 3

(6) Use Descartes’ Rule of Signs to find the maximum possible number of negative roots

( zeros ) of the given equation.

f ( x ) = 5 x ⁴ − 2 x ³ + 2 x ² − 5 x + 12

(a) 2 (b) 3 (c) 1 (d) 4 (e) 0

(7) Which logarithmic quantity is smaller?

(a) 2 log ( 1000 ) (b) log ₃ ( 243 ) (c) 0.5 ln ( 50 ) (d) log ₆ ( 216 ) (e) log ₅ ( 625 )

(8) Locate the vertex of the given parabolic function. f ( x ) = − 4 x ² + 32 x + 1

(a) ( − 4 , 385 ) (b) ( 4 , 21 ) (c) ( − 4 , 65 ) (d) ( 4 , 81 ) (e) ( 4 , 65 )

(9) Find the real solutions of this system of equations. x ² − y = 34

x ¹ + y = 8

(a) ( − 2 , 6 ) ; ( − 15 , 7 ) (b) ( 6 , − 2 ) ; ( − 7 , 5 )

(10) One of the solutions of the given equation is x = − 3 / 2 . Another solution is _____ .

2 x ²+ 5 x + 3 = 0

(a) − 2 (b) − 1 (c) − 3 (d) 4 (e) 2

₁₀

(11)

Find the following sum.

S ( − 2 i + 20 )

ⁱ^{= 1}

(a) 90 (b) − 2 (c) 88 (d) 92 (e) 2

(12) If a _n is an arithmetic sequence defined such as a ₁₀ = 60 and a ₁₅ = 90 , find a ₅ _.

(a) 40 (b) 20 (c) 30 (d) 15 (e) 45

(13) Determine the following sum: 36 + 37 + 38 + × × × + 120 + 121 + 122 + 123

(a) 6,855 (b) 6,873 (c) 6,837 (d) 6,996 (e) 6,960

(14) What is the value of z in the solution of this 3 by 3 system of equations?

− x − 1 y − 1 z = − 45

+ x − 1 y − 2 z = − 150

− x + 1 y + 1 z = + 85

(a) z = 0 (b) z = 40 (c) z = 65 (d) z = 60 (e) z = − 20

(15) A certain process obeys the decay equation: A = P e ⁻^{R T} . Find the value of A when

P is 50 , R is 0.05 , T is 10 , and e is approximately equal to 2.718281828.

Round your answer to four places to the right of the decimal point.

(a) 61.1826 (b) 30.3265 (c) 18.1582 (d) 475.6147 (e) 113.1515

(16) Compared to the graph of f ( x ) = 3 x ² , the graph of g ( x ) , shown below, is shifted _____ units horizontally to the left and vertically translated _____ unit downward

g ( x ) = 3 ( x + 2 ) ²− 1

(a) 2 ; 1 (b) 2 ; 3 (c) 3 ; 1 (d) 1 ; 2 (e) 3 ; 2

(17) Find the coordinates ( h , k ) of the center of this circle.

x ² + y ² − 4 x − 2 y − 4 = 0

(a) ( 4 , 3 ) (b) ( 2 , 1 ) (c) ( 0 , 3 ) (d) ( 1 , 3 ) (e) ( 1 , 2 )

(18) The function f ( x ) = 2 x − 4 is one - to - one. Its inverse f ⁻¹( x ) = _________ .

(a) 0.25 x + 4 (b) x + 2 (c) 0.5 x + 2 (d) − 0.5 x + 4 (e) − 0.5 x − 4

(19) In how many ways can Alice, Barry, Carol and Dino line - up to take a group photograph if Carol is to stand on the right - hand side?

(a) 3 (b) 6 (c) 12 (d) 24 (e) 8

(20) Solve the inequality. 1 < − 3 y − 2 < 4

(a) ( − 2 , − 1 ) (b) ( − 2 , 1 ) (c) ( − 2 , 1 ) (d) ( − 3 , − 2 ) (e) No solution

(21) Find the discriminant b ² − 4 a c of the quadratic equation shown below.

− 2 x ² − 10 x + 3 = 0

(a) − 124 (b) 76 (c) − 76 (d) 124 (e) − 112

(22) Solve the following exponential equation for x . 5 ^x^{+ 5} = 244,140,625

(a) 12 (b) 10 (c) 13 (d) 9 (e) 7

(23) If a graph is symmetric with respect to the x - axis, then for every point ( x , y ) on the graph, the point ( _____ , _____ ) is also on the graph.

(a) ( − x , − y ) (b) ( 0 , y ) (c) ( − x , y ) (d) ( x , − y ) (e) ( x , y )

(24) Determine whether the given expression has a value or values that must be excluded

from the domain of f ( x ) .

f ( x ) =

x ² − 4

x − 4

(a) only x = − 1 must be excluded (b) only x = 4 must be excluded

(25) Simplify the following expression into the general form of a complex number, namely

a + b i . 8 i ( − 5 + 3 i ) + 5 ( 3 − 4 i )

(a) − 33 − 60 i (b) 60 + 9 i (c) 60 − 9 i (d) 1 + 44 i (e) − 9 − 60 i

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