Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Transformations of Functions

Modeling with Functions Answers

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A rectangle with constant area has possible lengths and widths as shown in the table below. Width vs. Length of a RectangleWidth (w)Length (l)237.5418.75612.589.375Which equation can be used to find any corresponding length and width that fit the pattern in this table?

, where l is the length, w is the width, and k is a constant ()

, where l is the length, w is the width, and m and b are constants

, where l is the length, w is the width, and k is a constant

, where l is the length, w is the width, and a is a constant

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A new car sells for $25,000. The value of the car decreases by 15% each year. What is the approximate value of the car 5 years after it is purchased?

, or approximately $11,093

, or approximately $17,500

, or approximately $18,984

, or approximately $24,575

The amount of water pressure exerted on a scuba diver varies with depth. The graph below shows the relationship between pressure, p, in atmospheres, and depth, d, in ft.Depth of Water and Water PressureBased on the information in the graph, what is the water pressure at sea level?

atm

0 atm

1 atm

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below., where l is the length of the pendulum in feetWhat is the approximate length of a pendulum that takes seconds to swing back and forth?

1.72 ft

3.05 ft

38.40 ft

46.08 ft

A travel agency made the table below to represent the profits it makes on a certain vacation package.Number of People vs. ProfitNumber of People Who Buy the Package, xProfit per Person (in dollars), y1050020800309004080050500Which of the following explains the best model for the data in the table?

an absolute value function since the values increase and then decrease

an exponential function since the ratios of the y-values are about the same

a linear function since the profit per person changes by $30 for each additional person

a quadratic function since the points lie on a curve that is symmetric about the line x = 30

Kareem wants to write an equation for the data in the table below.xy–3–2–101What is the general form of the equation Kareem can use to represent the data?

y = m x + b

y = a b Superscript x

y = a x squared + b x + c

, where

A new car sells for $25,000. The value of the car decreases by 15% each year. What is the approximate value of the car 5 years after it is purchased?

, or approximately $11,093

, or approximately $17,500

, or approximately $18,984

, or approximately $24,575

Which type of function best models the data in the table below?xy244268110

inverse variation

linear

logarithmic

quadratic

The graph below represents the path of a grasshopper as it jumps.Which type of function models the data on the graph?

inverse variation

linear

square root

quadratic

A science teacher wrote the table of values below.Amount of Hydrogen vs. pHAmount of Hydrogen, x(in moles per liter)pH, f(x)12345Which function models the data in the table?

Ramiro drew the graph below.Which equation represents the data in the graph?

y = x squared minus 8 x + 16

y = 5.5 x squared minus 0.5 x + 4

y = x squared + 4 x + 4

y = 2.5 x squared minus 0.5 x + 4

The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. The stopping distances and speeds are shown in the table below.Stopping Distance of a Car vs. SpeedStopping Distance, d (in feet)Speed, s (in miles per hour)2017.894025.306030.988035.7810040.00Which equation best represents the data in the table?

s = 4 StartRoot d EndRoot

s = 0.37 d + 20

s = 13.7log(d)

s = StartFraction 1 Over 25 EndFraction d squared

Tasha invests $5,000 at 6% annual interest and an additional $5,000 at 8% annual interest. Thomas invests $10,000 at 7% annual interest. Which statement accurately compares Tasha’s and Thomas’s investments if interest is compounded annually?Compound interest formula: t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

Each person will have exactly the same amount over time because each invested $10,000 at an average interest rate of 7%.

Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Thomas’s investment will yield more from the start because he has more money invested at the average percentage rate.

Tasha’s investment will yield more at first because she invested some at a higher rate, but Thomas’s investment will yield more over the long run.

Janis was offered two different jobs when she graduated from college. She made the graph and table to show how much she would earn over time at each job.Earnings over Time for Job 1Earnings over Time for Job 2When will Janis’s salary be the same for job 1 and job 2, and how much will she be earning at that point?

The salaries will be the same in year 20, and she will be earning $80,000.

The salaries will be the same in year 16, and she will be earning $70,000.

The salaries will be the same in year 12, and she will be earning $60,000.

The salaries will be the same in year 10, and she will be earning $55,000.

The salaries will be the same in year 20, and she will be earning $80,000.

The salaries will be the same in year 16, and she will be earning $70,000.

The salaries will be the same in year 12, and she will be earning $60,000.

The salaries will be the same in year 10, and she will be earning $55,000.

Jordan uses a linear equation to model the data in a table. Which reasoning might Jordan have used in the decision to model the data with a linear equation?

The products of corresponding x- and y-values are equal.

The ratios of consecutive y-values are equal for evenly spaced x-values.

The y-values are the reciprocals of the corresponding x-values.

The change in y-values is constant for evenly spaced x-values.

A science teacher wrote the table of values below.Amount of Hydrogen vs. pHAmount of Hydrogen, x(in moles per liter)pH, f(x)12345Which function models the data in the table?

The height of an object after it is released can be modeled by the function , where t is the number of seconds after the object is released, v is the upward speed in feet per second at release, and s is the starting height in feet. If a quarterback throws a ball from his hand 6 feet in the air at an upward speed of 25 feet per second, how much time does his teammate have to catch the ball?

about 1.45 seconds

about 1.77 seconds

about 3 seconds

about 6 seconds

, where l is the length, w is the width, and k is a constant ()

, where l is the length, w is the width, and m and b are constants

, where l is the length, w is the width, and k is a constant

, where l is the length, w is the width, and a is a constant

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