Reporting Category 6: Rational Functions
Algebra 2: RC 6
2A.10A (S)
1. y=xn, where x>0 and n<0, which statement is valid for real values of y?
A. y>0 C. y<0
B. y=0 D. y≤0
2. Describe the transformation of the graph of f(x)=5x+b when b increases.
F. translated left H. translated right
G. translated up J. translated down
3. What are the vertical asymptotes of the function f(x)=4x²-1002x²+x-15 ?
A. x= -5, x=5 C. x= -3, x=52
B. x= -5, x=4, x=5 D. x= -3, x=52, x=203
4. a. Graph f(x)=xx+1 .
b. State the domain and range.
c. What are the vertical asymptote(s)?
d. What are the horizontal asymptote(s)?
Algebra 2: RC 6
2A.10A (S)
5. a. Graph f(x)=6x-2(x+3) .
b. State the domain and range.
c. What are the vertical asymptote(s)?
d. What are the horizontal asymptote(s)?
6. a. Graph f(x)=x²-25x-5 .
b. State the domain and range.
c. What are the vertical asymptote(s)?
d. What are the horizontal asymptote(s)?
7. The Curve of Agnesi is a bell-shaped curve that was discovered by Fermat nearly a hundred years before Agnesi.
a. Graph f(x)=a³x²+a² if a=4.
b. State the domain and range.
c. What are the vertical asymptote(s)?
d. What are the horizontal asymptote(s)?
Algebra 2: RC 6
2A.10B (S)
1. A train travels at one velocity V1 for a given amount of time t1 and then another velocity V2 for a different amount of time t2. The average velocity is given by the formula
V=V1t1+V2t2t1+t2
Let t1 be the independent variable and let V be the dependent variable. Draw the graph if V1=60 mph, V2=40 mph, and t2=8 hours. Find V when t1=9 hours.
2. For certain medicines, health care professionals may use Young’s rule,
C=yy+12 D,
to estimate the proper dosage for a child when the adult dosage is known. If C represents the child’s dose, D represents the adult’s dose, and y represents the child’s age in years, use Young’s Rule to estimate the dosage of amoxicillin for an eight year old child if the adult dose is 250 mg.
Graph C=yy+12 and note its shape, asymptotes, domain, and range.
3. When a car has a front-end collision, the objects in the car (including passengers) keep moving forward until the impact occurs. After impact, objects are repelled. Seat belts and airbags limit how far you are jolted forward. The formula for the velocity you are thrown backward is
Vf=m1-m2m1+m2 vi,
Where m1 and m2 are the masses of the two objects meeting and vi is the initial velocity. Let m1 be the independent variable and let Vf be the dependent variable. Graph the function if m2=7 kg and vi=5 m/s.
Find the value of Vf when the value of m1 is 5 kg.
Algebra 2: RC 6
2A.10C (S)
1. A chemical compound’s concentration in milligrams per liter during a reaction can be modeled by the function below, where t represents the number of seconds that have elapsed during the reaction.
f(t)=100t²+1
In this situation, what are the domain and range for this function?
A. Domain: t≥0, Range: 0<f(t)≤100
B. Domain: t≥0, Range: f(t)≥100
C. Domain: t≤0, Range: 0<f(t)≤100
D. Domain: t≤0, Range: f(t)≥100
2. A train travels at one velocity V1 for a given amount of time t1 and then another velocity V2 for a different amount of time t2. The average velocity is given by the formula
V=V1t1+V2t2t1+t2
Let t1 be the independent variable and let V be the dependent variable. If V1=60 mph, V2=40 mph, and t2=8 hours. State the domain and range.
3. For certain medicines, health care professionals may use Young’s rule,
C=yy+12 D,
to estimate the proper dosage for a child when the adult dosage is known. If C represents the child’s dose, D represents the adult’s dose, and y represents the child’s age in years, what is the domain and range of C=yy+12 ?
Algebra 2: RC 6
2A.10C (S)
4. When a car has a front-end collision, the objects in the car (including passengers) keep moving forward until the impact occurs. After impact, objects are repelled. Seat belts and airbags limit how far you are jolted forward. The formula for the velocity you are thrown backward is
Vf=m1-m2m1+m2 vi,
Where m1 and m2 are the masses of the two objects meeting and vi is the initial velocity. Let m1 be the independent variable and let Vf be the dependent variable. If m2=7 kg and vi=5 m/s, find the domain and range.
5. State a reasonable domain and range of y<x-4x-6 .
6. State a reasonable domain and range of y≥3x²+5x+6 .
Algebra 2: RC 6
2A.10D (S)
1. Most tunnels are drilled using tunnel-boring machines that begin at both ends of the tunnel. Suppose a new underwater tunnel is being built and one tunnel-boring machine alone can finish the tunnel in 4 years. A different type of machine can tunnel to the other side in 3 years. If both machines begin at opposite ends and work at the same time, when will the tunnel be finished?
2. A car travels 300 km in the same time that a freight train travels 200 km. The speed of the car is 20 km/h more than the speed of the train. Find the speed of the car and the speed of the train. (Hint: d=rt)
3. The Texas Junk Yard Company wants to build a brick wall to hide the area where they store wrecked cars from public view. One bricklayer can build this wall in 5 days. Another bricklayer can do the job in 4 days. If the company hires both of them to work together, how long will it take them to finish the wall?
4. During one-fourth of the time it took her to travel from Denver to Cheyenne, Alice drove in a snow storm at an average speed of 40 mph. She drove the rest of the time at an average speed of 65 mph. What was her average speed for the entire trip?
5. The ratio of 8 less than a number to 28 more than that number is 2 to 5. What is the number?
Algebra 2: RC 6
2A.10D (S)
6. The denominator of a fraction is one less than twice the numerator. If seven is added to both the numerator and the denominator, the resulting fraction has a value of 710 . Find the original fraction.
Algebra 2: RC 6
2A.10E (S)
1. Selena has scored 11 free throws in 20 attempts. Her coach has told her that she needs to bring her free throw average up to 70%. Selena wants to increase her average as quickly as possible. Determine the number of consecutive free throws Selena must score to bring her average up to at least 70%.
2. Solve x-2x < x-4x-6 .
3. Solve 2x3 – x+36 > 2.
4. Solve y+5 ≤ 6y .
5. Solve 5+7z8 – 15+3z10 < 2.
Algebra 2: RC 6
2A.10F (R)
1. A monthly cell phone plan charges $5.00 for the first 300 text messages and $0.15 for each additional message. On this plan, what is the number of text messages that must be used in a month in order to make the average cost per message $0.05?
A. 400 C. 900
B. 350 D. 500
2. How much pure juice and 20% juice should mix to make 4 quarts of 50% juice?
3. If Jason purchases two suits for $179 each and three suits that cost x dollars each. Find x so that the average price per suit is $185.00.
4. Class A has 15 students and an average height of 60”. Class B has 20 students. What is class B’s average height if the average height of both classes is 65”?
5. Suppose a professor counts quizzes as 10% of the final grade, homework 10%, exam 1 20%, exam 2 20%, and the final project 40%. Myra has an 80% quiz average, 89% homework average, 79% on exam 1, and 84% on exam 2. What does she have to earn on the final project in order to receive a final average of 85%?
Algebra 2: RC 6
2A.10G (S)
1. Architects have to consider how sound travels when designing large buildings such as theaters, auditoriums, or museums. Sound intensity I is inversely proportional to the square of the distance from the sound source d. If the sound intensity is 4 when the distance is 2, what is the sound intensity twice as far from the source?
2. How does the circumference of a circle vary with respect to its radius? What is the constant of variation?
3. When a person swims underwater, the pressure in his or her ears varies directly with the depth at which he or she is swimming. At 10 feet, the pressure is about 4.3 psi.
a. Find the pressure if the depth is 60 feet.
b. It is unsafe for amateur divers to swim where the water pressure is more than 65 psi. How deep can an amateur diver safely swim?
4. The current I in an electrical circuit varies inversely with the resistance R in the circuit. If a current of 2 amperes corresponds with 3 ohms of resistance, a resistance of 6 ohms would correspond with how many amperes?
Algebra 2STAAR Page 82