Math 112 - final exam

3.1.5 Determine the domain of the function 𝑅(𝑥) = √2 − 5𝑥 (A) [0.4, ∞) (B) (−∞, 0.4] (C) (0.4, ∞) (D) (−∞, 0.4) (E) [0, ∞)

(B) (−∞, 0.4]

1.2.2 Tina has $6.30 in nickels and quarters in her coin purse. she has a total of 54 coins. how many quarters does she have? a)18 b) 32 c) 24 d) 16 e) 36

18

1.1.1 Which ones of these equations is linear? a) 3x+2=4√x b) √4 x-3=3 c) 3x+ 1/x =2 d) x∧2-x=7 e) x^1/3 =7

√4 x-3=3

5.5.2 Solve for 𝑥: log9(𝑥 − 5) + log9(𝑥 + 3) = 1 𝑥=6,−4 only 𝑥 = 6 only 𝑥 = 11/2 only 𝑥 = −6,4 only 𝑥=4 only

𝑥 = 6 only

1.1.2 solve for x: 2x/x-3 +1=5/x-3 a) x=2/3 b) x=3/2 c) x=8/3 d) x=3/8 e) x=2

x= 8/3

3.3.1

(E) (0,3) and (− 3/2 , 0) only

5.1.4i. Determine the range of 𝐽(𝑥)=(1/3)^𝑥+2 (A) [2,∞) (B) (−∞,2] (C) (−∞,2) (D) (−∞,∞) (E) (2,∞)

(E) (2,∞)

5.6.6 Atmospheric pressure is related to height above sea level according to an exponential model. Suppose the pressure at 18,000 feet is half that at sea level. Find the value of k in the continuous model and explain what the value of k tells you. Find the equation and use it to estimate the pressure at 1000 feet, as a percentage of the pressure at sea level. (A) Less than 20%. (B) Between 20% and 40%. (C) Between 40% and 60%. (D) Between 60% and 80%. (E) More than 80%.

(E) More than 80%.

5.6.5 Suppose a turkey is removed from an oven when its inner temperature reaches 185∘F and placed into a 75∘F room to cool. After a half hour, the temperature has dropped to 150∘F. Use Newton's Law of Cooling model to determine when the turkey will cool to 100∘F. (A) Less than 1 hour. (B) Between 1 and 1.5 hours. (C) Between 1.5 and 2 hours. (D) Between 2 and 2.5 hours. (E) More than 2.5 hours.

(C) Between 1.5 and 2 hours.

5.6.4 A certain lake is stocked with 1000 fish. The population is growing according to the logistic curve: 𝑃 = 10,000 where t is measured in months since the lake was initially stocked. After how many months will the fish population be 2000? (A) Less than 2 month. (B) Between 2 and 4 months. (C) Between 4 and 6 months. (D)Between 6 and 8 months. (E) More than 8 months.

(C) Between 4 and 6 months.

2.4.2 Determine the 𝑦-intercept of the line passing through the point (−6, 5) and perpendicular to the line 𝑥/2 + 𝑦/3 + 1 = 0. (A) (0, 9) (B) (0, −7) (C) (0, −3) (D) (0 ,2) (E) (0, −4)

(A) (0, 9)

4.4.6 Factor 𝑅(𝑥) = 2𝑥^3 + 5𝑥^2 − 𝑥 − 6 completely given that 𝑥 − 1 is a factor of 𝑅(𝑥). The other factors are: (A) (2𝑥+3) and(𝑥+2) (B) (2𝑥−3) and(𝑥−2) (C) (3𝑥+1) and(𝑥−3) (D) (3𝑥−1) and(𝑥+3) (E) (2𝑥+1) and(𝑥+2)

(A) (2𝑥+3) and(𝑥+2)

3.2.3 Identify the interval(s) on which the function below is increasing.

(A) (3, ∞)

5.2.7 An invasive beetle was discovered in a small Pacific island 15 years ago. It is estimated that there are 12,400 beetles on the island now, with a relative growth rate of 16%. How many beetles will there be after another 15 years? (A) 136,687 beetles (B) 114,892 beetles (C) 1,064,538 beetles (D) 1,506,729 beetles (E) none of the above

(A) 136,687 beetles

1.4.4 Solve 3𝑥^2 − 2𝑥 = 8. The SUM of the solutions is: (A) 2/3 (B) −2/3 (C) 4/3 (D) −4/3 (E) None of these

(A) 2/3

1.5.6 It takes Julia 16 minutes longer to chop vegetables for soup than it takes Bob. Working together, they are able chop the vegetables in 15 minutes. How long will it take Julia to complete if she works by herself? (A) 40 min (B) 36 min (C) 30 min (D) 24 min (E) 20 min

(A) 40 min

4.2.4 A concert venue holds a maximum of 1000 people. With ticket prices at $30, the average attendance is 650 people. It is predicted that for each dollar the ticket price is lowered, approximately 25 more people attend. What is the maximum possible revenue from this concert? (A) Less than $20,000 (B) Between $20,000 and $24,000 (C) Between $24,000 and $28,000 (D) Between $28,000 and $32,000 (E) More than $32,000

(A) Less than $20,000

4.2.2 A rancher has 3,000 feet of fencing and wants to enclose a rectangular field with an internal fence parallel to one side, as shown below. What is the maximum total area that can be enclosed? (A) Less than 400,000 sq ft (B) Between 400,000 sq ft and 425,000 sq ft (C) Between 425,000 sq ft and 450,000 sq ft (D) Between 450,000 sq ft and 475,000 sq ft (E) More than 475,000 sq ft

(A) Less than 400,000 sq ft

5.2.4 Anna has a choice between two investment options for a $1000 gift she received. The first option earns 7.8% interest compounded continuously. The second option earns 7.9% interest compounded semi-annually. Which option would yield the greatest amount of money after 5 years and by how much? (A) Option 1, between $0 and $5 more. (B) Option 2, between $0 and $5 more. (C) Option 1, between $5 and $10 more. (D) Option 2, between $5 and $10 more.

(A) Option 1, between $0 and $5 more.

5.1.5 Determine a formula of the form 𝑦 = 𝐶 ∙ 𝑏^𝑥 for the exponential function graphed below. What is the value of 𝑏? (A) 𝑏 = 1/2 (B) 𝑏=2 (C) 𝑏=−2 (D) 𝑏=6 (E) 𝑏 = 1/6

(A) 𝑏 = 1/2

3.3.3 Give a rule for the function graphed below.

(A) 𝑓(𝑥)={3𝑥+4 𝑥≤−2 5𝑥−1 𝑥>−2

3.2.4 Use the graph of 𝑦 = 𝑓(𝑥) given below to determine the interval on which 𝑓(𝑥) is negative.

(B) (1,4)

4.1.2 Find the vertex of the quadratic function 𝑓(𝑥) = 3𝑥^2 − 24𝑥 + 2. (A) (4, −48) (B) (4, −46) (C) (−4,146) (D) (−4, −48) (E) None of these

(B) (4, −46)

5.6.2 Suppose Matt initially invests $3000 in an account bearing 4% interest compounded monthly. How long will it take for the deposit to double in value, rounded to the nearest 0.01? (A) 17.33 years. (B) 17.36 years. (C) 19.22 years. (D) 19.74 years. (E) none of these.

(B) 17.36 years.

4.1.6 Find a formula for a parabola whose vertex is at (−2, −1) and which goes through the point (0, 11). The coefficient of 𝑥2 is: (A) 6 (B) 3 (C) 5/2 (D) 1 (E) −3

(B) 3

3.3.2 i. Consider the piecewise function 𝑓(𝑥) evaluate f(-3) (A) 5+√10 (B) 9 (C) −4 (D) √10 (E) undefined

(B) 9

5.6.3 Radioactive bismuth has a half-life of 5 days. Estimate how much of a 200 gram sample will be radioactive in 13 days. (A) Less than 20 grams. (B) Between 20 and 40 grams. (C) Between 40 and 60 grams. (D) Between 60 and 80 grams. (E) More than 80 grams.

(B) Between 20 and 40 grams.

1.5.2 A stone thrown downward from a height of 274.4 meters. The distance it travels in t seconds is given by the function 𝑠(𝑡) = 4.9𝑡^2 + 49𝑡. How long will it take the stone to hit the ground? (A) Less than 3 seconds (B) Between 3 and 5 seconds (C) Between 5 and 7 seconds (D) Between 7 and 9 seconds (E) More than 9 seconds

(B) Between 3 and 5 seconds

3.4.14 Describe the function 𝑦 = − 23 𝑓(𝑥) + 5 as a transformation of the function 𝑦 = 𝑓(𝑥). (A) Stretch horizontally, reflect across 𝑥-axis, shift left 5 (B) Compress vertically, reflect across 𝑥-axis, shift up 5 (C) Stretch vertically, reflect across 𝑥-axis, shift up 5 (D) Compress vertically, reflect across 𝑦-axis, shift up 5 (E) Stretch horizontally, reflect across 𝑦-axis, shift up 5

(B) Compress vertically, reflect across 𝑥-axis, shift up 5

3.5.1 Use the functions 𝑔(𝑥) and h(𝑥) given below to determine (h ∘ 𝑔)(3).

(B) −1

5.3.3 Evaluate the expression log2 1/8. (A) 1/3 (B) −3 (C) 1/4 (D) −4 (E) 0

(B) −3

4.3.1 Determine which one of the following represents a polynomial function. (A) 𝑃(𝑥) = 4𝑥^2 − 3𝑥−1 (B) 𝑄(𝑥)=√5𝑥^4−4𝑥^3+6 (C) 𝑅(𝑥) = 7𝑥+2𝑥^2−3𝑥^4/𝑥 (D) 𝑆(𝑥)=𝑥^4−3𝑥^1/3+1 (E) 𝑇(𝑥)=7𝑥^2−√𝑥+𝑥

(B) 𝑄(𝑥)=√5𝑥^4−4𝑥^3+6

3.6.2 Find the inverse of the function 𝑓(𝑥) = 𝑥−1 . 2𝑥+3 (A) 𝑓^−1(𝑥) = −4/ 2𝑥−1 (B) 𝑓^−1(𝑥)=−3𝑥−1/2𝑥−1 (C) 𝑓^−1(𝑥) = 𝑥+1/0.5𝑥−3 (D) 𝑓^−1(𝑥)=−2𝑥+3/𝑥−1 (E) None of these

(B) 𝑓^−1(𝑥)=−3𝑥−1/2𝑥−1

5.2.2 Solve for 𝑥: ^3√𝑒^5 = 𝑒^x-1 (A) 𝑥=−14 (B) 𝑥=8/3 (C) 𝑥=2/3 (D) 𝑥 = 8/5 (E) 𝑥 = −2/5

(B) 𝑥=8/3

1.4.5 Solve (𝑥 − 2)(𝑥 + 4) = 1. The largest real solution is: (A) 𝑥=3 (B) 𝑥=−1+√10 (C) 𝑥=−1+2√2 (D) 𝑥=−2+2√2 (E) 𝑥=−2+√10

(B) 𝑥=−1+√10

4.3.6 Determine a possible equation for the polynomial functions graphed below. (A) 𝑦=12(𝑥+2)(𝑥−2)^2 (B) 𝑦=12𝑥(𝑥+2)(𝑥−2)^2 (C) 𝑦=16𝑥(𝑥−2)(𝑥+2)^2 (D) 𝑦=16(𝑥−2)(𝑥+2)^2 (E) None of these

(B) 𝑦=12𝑥(𝑥+2)(𝑥−2)^2

3.4.16 If the point (2,5) is on the graph of 𝑦 = 𝑔(𝑥), determine a point that MUST be on the graph of 𝑦 = 2𝑔 (1/5 𝑥) + 3. (A) ( 2/5 , 13 ) (B) (4,4) (C) (10,13) (D) (10, 11/2) (E) (4,13)

(C) (10,13)

5.3.7 Find the domain of the logarithmic function 𝑓(𝑥) = log(3 − 2𝑥). (A) (−∞,32] (B) [32,∞) (C) (−∞,32) (D) (32,∞) (E) None of these.

(C) (−∞,32)

4.4.2 ii Determine the remainder when 𝑓(𝑥) = −3𝑥^4 − 8𝑥^3 + 5𝑥 + 11 is divided by 𝑥 + 2. (A) 33 (B) 5 (C) 17 (D) −7 (E) None of these

(C) 17

1.2.9 Suppose a journeyman and apprentice carpenter are working on making cabinets. The journeyman is twice as fast as his apprentice. If they complete one cabinet in 14 hours, how many hours does it take for the journeyman working alone to make one cabinet? (A) 28.2 hours (B) 25 hours (C) 21 hours (D) 18.5 hours (E) 14.7 hours

(C) 21 hours

3.1.4 Use the function 𝑓(𝑥) = 3𝑥^2 − 5𝑥 to evaluate 𝑓(h+4)−𝑓(4)/h. (A) 3h2−29h+56/ h (B) 3h −19h+56/h (C) 3h+19 (D) 3h + 56 (E) None of these

(C) 3h+19

5.1.10 Suppose Melissa invests $9400 into a high-yield savings account that pays 5.7% interest compounded quarterly. Her brother, Billy, invests $10,200 into a different account that pays 4.8% compounded monthly. If no other investments are made, who will have more money in their account at the end of 10 years? How much more money will that person have? (A) Melissa will have $1 to $50 more than Billy. (B) Billy will have $1 to $50 more than Melissa. (C) Melissa will have $50 to $100 more than Billy. (D) Billy will have $50 to $100 more than Melissa.

(C) Melissa will have $50 to $100 more than Billy.

3.3.2 ii. What is the range of the function 𝑓(𝑥) (A) [0, ∞) (B) [1, ∞) (C) [−1, ∞) (D) (2,∞) (E) (−∞, ∞)

(C) [−1, ∞)

4.3.2 Consider the polynomial function graphed below. Determine whether the leading coefficient is positive or negative and whether the degree is even or odd. (A) leading coefficient is positive, degree is odd (B) leading coefficient is positive, degree is even (C) leading coefficient is negative, degree is odd (D) leading coefficient is negative, degree is even

(C) leading coefficient is negative, degree is odd

1.4.6 Solve 1/2 (𝑥 + 1)^2 − 3 = 0. The SUM of the solutions is: (A) −1 (B) 1 (C) −2 (D) 2 (E) 2√6

(C) −2

4.6.4 Find the equation of the rational function graphed below. (A) 𝑓(𝑥) = 2𝑥+3/𝑥−3 (B) 𝑓(𝑥) = 2𝑥+3/𝑥+3 (C) 𝑓(𝑥) = 2𝑥^2+𝑥−3/𝑥^2−4𝑥+3 (D) 𝑓(𝑥)=2𝑥^2+5𝑥+3/𝑥^2−2𝑥−3 (E) None of these

(C) 𝑓(𝑥) = 2𝑥^2+𝑥−3/𝑥^2−4𝑥+3

3.5.6 Supposeh(𝑥)=(𝑓∘𝑔)(𝑥). Ifh(𝑥)=(𝑥^2 −1)3 +4 and𝑔(𝑥)=𝑥^2, find𝑓(𝑥). (A) 𝑓(𝑥)=𝑥^3+4 (B) 𝑓(𝑥)=𝑥+4 (C) 𝑓(𝑥)=(𝑥−1)^3 +4 (D) 𝑓(𝑥)=𝑥^3+3 (E) 𝑓(𝑥)=(𝑥−1)^3

(C) 𝑓(𝑥)=(𝑥−1)^3 +4

4.3.5 ii. Which one of the following is a polynomial function of degree 5 with zeros at 𝑥 = 2 and 𝑥=−7? (A) 𝑓(𝑥) = −𝑥(𝑥 + 7)^2(𝑥 − 2)^3 (B) 𝑓(𝑥) = −𝑥(𝑥 − 7)^3(𝑥 + 2)^2 (C) 𝑓(𝑥)=−4(𝑥2+3)(𝑥+7)2(𝑥−2) (D) 𝑓(𝑥)=−4(𝑥−7)^2(𝑥+2)^3 (E) 𝑓(𝑥) = −4(𝑥2 + 3)(𝑥 + 7)^2(𝑥 − 2)^2

(C) 𝑓(𝑥)=−4(𝑥2+3)(𝑥+7)2(𝑥−2)

5.4.5 Solve for 𝑥: log2(3) = log2(5𝑥) − log2(𝑥 + 1) (A) 𝑥 = 1/2 (B) 𝑥 = 1/4 (C) 𝑥 = 3/2 (D) 𝑥 = 3/8

(C) 𝑥 = 3/2

2.3.2 Determine an equation in slope-intercept form for the line graphed below. (A) 𝑦=𝑥−1 (B) 𝑦=𝑥+9 (C) 𝑦=−4𝑥−11 (D) 𝑦=−4𝑥+5 (E) None of these

(C) 𝑦=−4𝑥−11

5.2.6 The population of a city can be measured by 𝑃(𝑡) = 12,500𝑒^0.02𝑡, where t represents time in years after 1985. What does the model predict the population to be in the year 2020? (A) less than 10,000 (B) between 10,000 and 20,000 (C)between 20,000 and 30,000 (D)between 30,000 and 40,000 (E) more than 40,000

(C)between 20,000 and 30,000

5.2.3 Dmitry invests $3200 in a savings account that earns 4.6% interest compounded continuously. How much money would Dmitry have in the account after 3.5 years? (A) $639.64 (B) $2724.13 (C) $3745.51 (D) $3758.99 (E) $16,008.99

(D) $3758.99

5.1.11 Phillip wants to have $10,000 in 6 years, so he will place money into a savings account that pays 3.2% interest compounded weekly. How much should Phillip invest now to have $10,000 in 6 years? (A) $1,466.07 (B) $1,474.72 (C) $8,253.07 (D) $8,253.56 (E) $12,115.99

(D) $8,253.56

3.4.11 The graph of 𝑦 = 𝑓(𝑥) is given below. Sketch a graph of 𝑦 = 𝑓 (1/2 𝑥). What are the 𝑥- intercept(s) of 𝑦 = 𝑓 (1/2 𝑥)?

(D) (−2,0)and(4,0)

1.2.7 Two motorcycles travel toward each other from Chicago and Indianapolis (about 350km apart). One is travelling 110 km/hr, the other 90 km/hr. If they started at the same time, after how many hours will they meet (A) 0.5 hours (B) 1.25 hours (C) 1.5 hours (D) 1.75 hours (E) 2.25 hours

(D) 1.75 hours

4.4.1 Determine the quotient when 𝑓(𝑥) = 2𝑥^3 − 4𝑥^2 + 6𝑥 − 8 is divided by 𝑥^2 + 𝑥 − 2. (A) 𝑥−5 (B) 2𝑥−2 (C) 𝑥+3 (D) 2𝑥−6 (E) None of these

(D) 2𝑥−6

1.5.7 Maria traveled upstream along a river in a boat a distance of 39 miles and then came right back. If the speed of the current was 1.3 mph and the total trip took 16 hours, determine the speed of the boat relative to the water. (A) 6.5 mph (B) 3.9 mph (C) 4.9 mph (D) 5.2 mph (E) 7.4 mph

(D) 5.2 mph

1.5.3 Amy travels 450 miles in her car at a certain speed. If the car had gone 15 mph faster, the trip would have taken 1 hour less. Determine the speed of Amy's car. (A) 60 mph (B) 65 mph (C) 70 mph (D) 75 mph (E) 80 mph

(D) 75 mph

4.2.1 A stone is thrown upward; its height in meters 𝑡 seconds after release is given by h(𝑡) = −4.9𝑡^2 + 49𝑡 + 277.4. How long will it take the stone to hit the ground? (A) Less than 9 seconds (B) Between 9 and 11 seconds (C) Between 11 and 13 seconds (D) Between 13 and 15 seconds (E) More than 15 seconds

(D) Between 13 and 15 seconds

1.2.6 A boat travels down a river with a current. Travelling with the current, a trip of 66 miles takes 3 hours while the return trip travelling against the current takes 4 hours. How fast is the current? (A) Between 1.0 and 1.5 mph (B) Between 1.5 and 2.0 mph (C) Between 2.0 and 2.5 mph (D) Between 2.5 and 3.0 mph (E) Between 3.0 and 3.5 mph

(D) Between 2.5 and 3.0 mph

5.6.1 The world population has been growing roughly exponentially for the past 30 years. In 1987, the world population was approximately 5 billion. In 1998, the world population was approximately 6 billion. Find an exponential equation of the form 𝑦 = 𝐶𝑒𝑘𝑡 which models the world population with 𝑡 representing the number of years since 1987. What does this model predict the population was in 2010? (A) Less than 6 billion. (B) Between 6 and 6.5 billion. (C) Between 6.5 and 7 billion. (D) Between 7 and 7.5 billion. (E) More than 7.5 billion.

(D) Between 7 and 7.5 billion.

3.6.3 ii. Determine the value of 𝑓^−1(2) for the function 𝑓 whose graph is shown below. (A) 0 (B) 2 (C) −2 (D) Undefined (E) None of these

(D) Undefined

5.4.1 Use properties of logarithms to expand the expression as much as possible: ln (𝑥𝑦^3)/ 3𝑒^𝑥 (A) ln(𝑥) + ln(𝑦) − 𝑥 (B) ln(𝑥) + ln(𝑦) + 𝑥 (C) ln(𝑥)+3ln(𝑦)−3+𝑥 (D) ln(𝑥) + 3ln(𝑦) − ln(3) − 𝑥 (E) ln(𝑥) + 3ln(𝑦) − ln(3) + 𝑥

(D) ln(𝑥) + 3ln(𝑦) − ln(3) − 𝑥

3.6.3 i. Determine the value of 𝑓^−1(2) for 𝑓(𝑥) = 𝑥−1/ 2𝑥+3 (A) 1/7 (B) −3/7 (C) 7 (D) −7/3 (E) None of these

(D) −7/3

5.1.7 The table below gives values for a function of the form 𝑦 = 𝐶 ∙ 𝑏𝑥. Determine the values of 𝐶 and 𝑏. (A) 𝐶=3/2,𝑏=8 (B) 𝐶=16/3,𝑏=2/3 (C) 𝐶=8,𝑏=2/3 (D) 𝐶 = 16/3, 𝑏 = 3/2 (E) 𝐶=8, 𝑏=3/2

(D) 𝐶 = 16/3, 𝑏 = 3/2

3.6.1 Determine which one of the functions described below represents a one-to-one function. (A) 𝑔 is the function that assigns to each Math 112 student his/her Math 112 section number (B) 𝑆 is the function that assigns to each UA student the last four digits of his/her social security number (C) 𝑅(𝑥)={ −2𝑥 𝑥≤0 √𝑥−1 𝑥>0 (D) 𝑅(𝑥)={ −2𝑥 𝑥≤0 −√𝑥−1 𝑥>0

(D) 𝑅(𝑥)={ −2𝑥 𝑥≤0 −√𝑥−1 𝑥>0

3.1.7 Which one of the following functions has domain all real numbers except 𝑥 = −3 and 𝑥 = 1 ? (A) 𝑓(𝑥)=√𝑥^2+2𝑥−3 (B) 𝑓(𝑥)= 𝑥/𝑥^2+2𝑥−3 (C) 𝑓(𝑥) = 𝑥^2+2𝑥−3/𝑥 (D) 𝑓(𝑥)= 𝑥/ 𝑥^2+2𝑥−3 (E) 𝑓(𝑥)=√ 1/ 𝑥^2+2𝑥−3

(D) 𝑓(𝑥)= 𝑥/ 𝑥^2+2𝑥−3

4.4.5 Determine the value of the constant k so that 𝑥 − 2 is a factor of the function 𝑔(𝑥)=−𝑥^3 +𝑘𝑥^2 −4𝑥+10. (A) 𝑘 = −5/2 (B) 𝑘=−6 (C) 𝑘=4 (D) 𝑘 = 3/2 (E) None of these

(D) 𝑘 = 3/2

4.4.7 Determine the zeros of 𝑃(𝑥) = 4𝑥^3 + 16𝑥^2 − 23𝑥 − 15. (A) 𝑥 = −5, 𝑥 = − 1/3, and 𝑥 = 1/2 only (B) 𝑥 = 5, 𝑥 = − 1/2, and 𝑥 = 3/2 only (C) 𝑥 = −5, 𝑥 = 1/2, and 𝑥 = − 3/2 only (D) 𝑥 = −5, 𝑥 = − 1/2, and 𝑥 = 3/2 only (E) 𝑥 = 5, 𝑥 = 1/2, and 𝑥 = − 3/2 only

(D) 𝑥 = −5, 𝑥 = − 1/2, and 𝑥 = 3/2 only

3.2.1 Determine the zeros of 𝑝(𝑥) = 𝑥^2−𝑥/ 𝑥^2−𝑥−6 (A) 𝑥 = 1 only (B) 𝑥=−2 and𝑥=3 only (C) 𝑥=−2,𝑥=3,𝑥=0 and𝑥=1 (D) 𝑥=0 and𝑥=1only (E) 𝑥=0only

(D) 𝑥=0 and 𝑥=1 only

5.1.4 ii. Determine the asymptote for 𝐿(𝑥) = −2 ∙ 4^𝑥−3 + 5. (A) 𝑥 = 3 (B) 𝑦=10 (C) 𝑦 = −10 (D) 𝑦 = 5 (E) 𝑦=4

(D) 𝑦 = 5

2.3.5 Determine an equation for the horizontal line passing through the point (− 9/2 , 15/2). (A)𝑥=−9/2 (B) 𝑥=15/ 2 (C) 𝑦=−9/2 (D) 𝑦=15/2 (E) None of these

(D) 𝑦=15/2

4.1.3 Find a formula for the parabola graphed below. (A) 𝑦=(𝑥+1)(𝑥−2) (B) 𝑦=−(𝑥−1)(𝑥+2) (C) 𝑦=2(𝑥−1)(𝑥+2) (D) 𝑦=−(𝑥+1)(𝑥−2) (E) 𝑦=−2(𝑥+1)(𝑥−2)

(D) 𝑦=−(𝑥+1)(𝑥−2)

5.2.5 Arturo wants to have $15,000 in 6 years, so he will place money into a savings account that pays 3.7 % interest compounded continuously. How much should Arturo invest now to have $15,000 in 6 years? Check your answer. (A) $12,061.98 (B) $1629.14 (C) $138,109.96 (D) $18,728.57 (E) $12,013.73

(E) $12,013.73

3.5.5 Use the functions 𝑓(𝑥) = 𝑥^2 − 5 and h(𝑥) = √𝑥 + 1 to determine (h ∘ 𝑓)(𝑥). What is the domain of (h ∘ 𝑓)(𝑥) ? (A) (−∞, ∞) (B) (−1, ∞) (C) (4, ∞) (D) (2, ∞) (E) (−∞, −2] ∪ [2, ∞)

(E) (−∞, −2] ∪ [2, ∞)

3.5.3 Consider the functions 𝑓(𝑥) = 𝑥−1/x and 𝑔(𝑥) = 𝑥−2/x+5. Find (𝑓 ∘ 𝑔)(𝑥). (A) (𝑓∘𝑔)(𝑥)=− 7/𝑥^2+5𝑥 (B) (𝑓 ∘ 𝑔)(𝑥) = 𝑥^2−3𝑥+2/ 𝑥^2+5𝑥 (C) (𝑓 ∘ 𝑔)(𝑥) = −𝑥−1/6𝑥−1 (D) (𝑓 ∘ 𝑔)(𝑥) = −𝑥−1/ 𝑥^2+5𝑥 (E) (𝑓∘𝑔)(𝑥)=− 7/x-2

(E) (𝑓∘𝑔)(𝑥)=− 7/x-2

1.2.8 Suppose it takes Mike 3 hours to grade one set of homework and it takes Jenny 2 hours to grade one set of homework. If they grade together, how long will it take to complete one set of homework? (A) 2.5 hours (B) 2 hours (C) 1.8 hours (D) 1.5 hours (E) 1.2 hours

(E) 1.2 hours

1.5.5 The length of a rectangle is 7 centimeters longer than the width. If the diagonal of the rectangle is 17 centimeters, determine the length. (A) 5cm (B) 7cm (C) 8cm (D) 12 cm (E) 15 cm

(E) 15 cm

4.4.2i Determine the remainder when𝑓(𝑥)=𝑥3+5𝑥2−7 is divided by 𝑥−3. (A) 17 (B) −25 (C) −13 (D) 79 (E) 65

(E) 65

4.2.3 Suppose a sunglass manufacturer determines the demand function for a certain line of sunglasses is given by 𝑝=50− 1/4000 𝑥, where𝑝is the price per pair and 𝑥 is the number of pairs sold. The fixed cost of producing a line of sunglasses is $25,000 and each pair of sunglasses costs $3 to make. How many sunglasses should be produced to maximize profit? (A) 100,000 sunglasses (B) 87,000 sunglasses (C) 188,000 sunglasses (D) 200,000 sunglasses (E) 94,000 sunglasses

(E) 94,000 sunglasses

3.2.2 Find the domain and range of the function shown in the graph below:

(E) Domain: [−4,4) Range: [−5,4]

3.4.2 Given the graph of 𝑦 = 𝑓(𝑥) below, what is the domain of 𝑓(𝑥 − 3) − 2?

(E) [1,6]

5.3.1 Change the exponential equation 3−2 = 19 into logarithmic form. (A) log−2(3) = 1/9 (B) log3(−2) = 1/9 (C) log1/9(3) = −2 (D) log1/9 3 = −2 (E) log3(1/9) = −2

(E) log3(1/9) = −2

4.1.4 Find a formula for a parabola that goes through the points (−5, 0), (3, 0) and (1, 16). (A) 𝑓(𝑥)=4/3(𝑥+5)(𝑥+3) (B) 𝑓(𝑥)=−4/3(𝑥−5)(𝑥+3) (C) 𝑓(𝑥)=−(𝑥−5)(𝑥+3) (D) 𝑓(𝑥)=−(𝑥+5)(𝑥−3) (E) 𝑓(𝑥)=−4/3(𝑥+5)(𝑥−3)

(E) 𝑓(𝑥)=−4/3(𝑥+5)(𝑥−3)

3.2.11 Which of the following represents an odd function? (A) 𝑓(𝑥)=7𝑥^3+5𝑥+1 (B) 𝑔(𝑥)=√4−𝑥^2 (C) h(𝑥)= 𝑥/𝑥^3+1 (D) 𝑘(𝑥)=|𝑥−7| (E) 𝑙(𝑥)= 2𝑥/ 𝑥^2+10

(E) 𝑙(𝑥)= 2𝑥/ 𝑥^2+10

4.3.5 i Determine the zeros of the polynomial 𝑅(𝑥) = 𝑥(𝑥 + 3)2(𝑥 − 2)3, and their multiplicities. (A) 𝑥 = 0 (multiplicity 1), 𝑥 = 3 (multiplicity 1), and 𝑥 = −2 (multiplicity 1) only (B) 𝑥 = −3 (multiplicity 2) and 𝑥 = 2 (multiplicity 3) only (C) 𝑥 = 3 (multiplicity 2) and 𝑥 = −2 (multiplicity 3) only (D) 𝑥=0(multiplicity1),𝑥=3(multiplicity2)and𝑥=−2(multiplicity3)only (E) 𝑥 = 0 (multiplicity 1), 𝑥 = −3 (multiplicity 2) and 𝑥 = 2 (multiplicity 3) only

(E) 𝑥 = 0 (multiplicity 1), 𝑥 = −3 (multiplicity 2) and 𝑥 = 2 (multiplicity 3) only

2.4.3 Determine an equation for the line passing through the point (−4, −3) and parallel to the vertical line 3𝑥 + 4 = 0. (A) 𝑥=−4/3 (B) 𝑦=−3 (C) 𝑦=3𝑥+9 (D) 𝑦=−1/3𝑥−13/3 (E) 𝑥=−4

(E) 𝑥=−4

3.1.3 Which one of the following represents y as a function of x? (A) 𝑥^2+𝑦^2=9 (B) 𝑥^3+1+𝑦^4=0 (C) 𝑦=±√𝑥−5 (D) 2𝑥=5+𝑦^2 (E) 𝑥𝑦−4𝑦=7

(E) 𝑥𝑦−4𝑦=7

4.6.5 Determine the equation of a rational function if the zero of the function is 𝑥 = 4, the 𝑦- intercept is (0, −2), and the equations of the asymptotes are 𝑥 = 2 and 𝑦 = −1. (A) 𝑦= −𝑥−4/𝑥−2 (B) 𝑦= 𝑥−4/𝑥−2 (C) 𝑦= −𝑥−4/𝑥+2 (D) 𝑦=𝑥−4/𝑥−2 (E) 𝑦 = −𝑥+4/𝑥−2

(E) 𝑦 = −𝑥+4/𝑥−2

3.1.1 Determine which one the following represents y as a function of x.

A

3.1.2 Determine which one of the following represents y as a function of x.

A

3.2.10 Complete the table of values if the function is even. The missing values, in order from left to right in the table, are: (A) −3 and 5 (B) 3 and −5 (C) 3 and 5 (D) 1 and −2 (E) −1 and 2

A

3.2.8 Which one of the functions graphed below is neither even nor odd?

A

5.5.1

A

1.2.5 A chemist wants to strengthen her 40L stock of 10% solution of acid to 20%. How much 24% solution does she have to add to the 40L of 10% solution in order to obtain a mixture that is 20% acid? A) Less than 82 liters (B) Between 82 and 87 liters (C) Between 87 and 92 liters (D) Between 92 and 97 liters (E) More than 97 liters

More than 97 liters

3.5.2 The graphs of the functions 𝑓(𝑥) and 𝑔(𝑥) are shown below. Use the graphs to find the domain of f/g.

[−2, −1) ∪ (−1,5) ∪ (5,9)

5.4.2 Rewrite as a single logarithm: 2 log2(𝑥) + log2(𝑦) − 4 log2(𝑃) − 12 log2(𝑄) + log2(𝑧)

a

1.2.3 a company produces a pair of skates for $43.53 and sells each pair for $89.95. if the fixed costs are $742.72, how many pairs must the company produce to break even? a)between 9-13 b) between 13-17 c)between 17-21 d)between 21-25 e)more than 25

between 13-17

1.2.4 a premium mix of nuts costs $12.99 per pound, while almost cost $6.99 per pound. A shop owner adds almonds into the premium ix to get 09 pounds of nuts that costs $10.99 per pound. how many pounds of almonds did she add?

between 25 and 35 pounds

4.6.2 Find the horizontal or slant asymptote, if one exists, for the rational functions. i. 𝑝(𝑥)=2−3𝑥/𝑥+1 (A) Horizontal asymptote: 𝑦 = −3 (B) Horizontal asymptote: 𝑦 = 2 (C) Horizontal asymptote: 𝑦 = 2/3 (D) Horizontal asymptote: 𝑦 = 3/2 (E) Horizontal asymptote: 𝑦 = −1 ii. 𝑅(𝑥) = 2𝑥+1 𝑥2−16 (A)Slant asymptote: 𝑦 = 0.5𝑥 − 0.25 (B) Slant asymptote: 𝑦 = 2𝑥 (C) Horizontal asymptote: 𝑦 = 2 (D) Horizontal asymptote: 𝑦 = 0 (E)Horizontal asymptote: 𝑦 = −1/2 iii. 𝐿(𝑥) = 𝑥2−5𝑥+1/𝑥+1 Horizontal asymptote: 𝑦 = 0 Horizontal asymptote: 𝑦 = −1 Slant asymptote: 𝑦 = 𝑥 − 4 Slant asymptote: 𝑦 = 𝑥 Slant asymptote: 𝑦 = 𝑥 − 6

i. (A) Horizontal asymptote: 𝑦 = −3 ii. (D) Horizontal asymptote: 𝑦 = 0 iii. Slant asymptote: 𝑦 = 𝑥 − 6

4.6.1 Find the vertical asymptote(s) and removable discontinuity (hole), if any, of the rational functions. i. 𝐿(𝑥) = 𝑥^2+5𝑥−6 𝑥+1 (A) Vertical asymptote: 𝑥 = 1 only (B) Vertical asymptote: 𝑥 = −1 only (C) Vertical asymptotes: 𝑥 = 1 and 𝑥 = −6 (D) Vertical asymptote: 𝑥 = −6 only (E) There are no vertical asymptotes. ii. 𝐹(𝑥) = 𝑥^2−1/ 𝑥^2−𝑥−2 (A) Vertical asymptote at 𝑥 = −1; hole at 𝑥 = 2 (B) Vertical asymptotes at 𝑥 = 2 and 𝑥 = −1 (C) Vertical asymptote at 𝑥 = 2; hole at 𝑥 = −1 (D) Vertical asymptotes at 𝑥 = 1 and 𝑥 = −1 (E) Vertical asymptote at 𝑥 = 1; hole at 𝑥 = −1

i. (B) Vertical asymptote: 𝑥 = −1 only ii. (C) Vertical asymptote at 𝑥 = 2; hole at 𝑥 = −1

5.5.3 Solve each equation exactly. i. 140(1/2)^t/4 =350 (A) 𝑡 = 4 log1(5) (B) 𝑡=4log1/2(5/2) (C) 𝑡 = 4 log5/2(1/2) (D) 𝑡=4log5(2) ii. 3log(𝑢 − 7) = 6 (A) 𝑢 = 107 (B) 𝑢 = 93 (C) 𝑢 = 1007 (D) 𝑢 = 993 iii. 20(100 − 𝑒^𝑥/2) = 500 (A) 𝑥=2ln4 (B) 𝑥=ln(75/2) (C) 𝑥=2ln(75) (D) 𝑥 = 2 ln(125) iv. 2= 8/1+100𝑒^−3𝑡 (A) 𝑡 = − ln ( 1/100) (B) 𝑡=1/3ln(1/20) (C) 𝑡=−ln(3/20) (D) 𝑡 = −3 ln ( 3/100) (E) 𝑡=−1/3ln(3/100)

i. (B) 𝑡=4log1/2(5/2) ii.(A) 𝑢 = 107 iii. (C) 𝑥=2ln(75) iv.(E) 𝑡=−1/3ln(3/100)

5.3.8 Sketch the graph of each transformation. Determine the equation(s) of the asymptote(s). i. ln(𝑥−1)+3 (A) 𝑥=1,𝑦=3 (B) 𝑥=−1,𝑦=3 (C) 𝑥=1only (D) 𝑥=−1only (E) 𝑦=3only ii. log4(3𝑥 + 2) (A) 𝑥=−23 only (B) 𝑥=0only (C) 𝑦=0only (D) 𝑦=−23 only (E) 𝑥=0,𝑦=−23

i. (C) 𝑥=1only ii. (A) 𝑥=−23 only