F-BF/IF/LE Word Problems

F-BF/IF/LE Word Problems

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Multiple Choice

A restaurant host earns $10 for each hour worked up to 40 hours each week and $15 for each additional hour worked over 40 hours. If x represents the total number of hours the restaurant host works, which function, f(x), represents the total amount the restaurant host would earn if working for more than 40 hours?

• $$f(x)=400+15(x−40)$$

• $$f(x)=400+15(x+40)$$

• $$f(x)=600+10(x−40)$$

• $$f(x)=600+10(x+40)$$

Multiple Choice

A company pays employees $12 per hour and 1.5 times the hourly rate for overtime, which is any amount over 40 hours that an employee works in a week. The company deducts 15% of the weekly paycheck for taxes.

If one employee’s weekly paycheck is $825.75 before taxes, approximately how many hours of overtime did the employee work that week?

• 12.33 hours

• 19.21 hours

• 8.83 hours

• 14.48 hours

Multiple Choice

A student wants to buy a violin and take lessons.

The violin costs $95.

The lessons cost $65 per hour.

Which equation represents the total cost of the violin and lessons, T, based on the number of hours, h, of lessons?

• $$T(h)=65h−95$$

• $$T(h)=65h+95$$

• $$T(h)=95h−65$$

• $$T(h)=95h+65$$

Multiple Choice

The value of a computer decreases by 35% each year. If the computer was initially sold for $1,250, which function represents the value, V(t), of the computer t years after being sold?

• $$V(t)=1,250(1.35)^t$$

• $$V(t)=1,250(.35)^t$$

• $$V(t)=1,250(0.65)^t$$

• $$V(t)=1,250(1.65)^t$$

Multiple Select

The function  $$h(x)=−16x^2+48x+1$$  represents the height, in feet, of a toy rocket x seconds after being launched. Which two statements are true?

• The rocket attains its highest elevation after 37 seconds.

• The rocket hits the ground after approximately 3 seconds.

• The rocket is launched from an initial height of 1 foot.

• The rocket is launched from an initial height of 0 feet.

• The rocket’s highest elevation is approximately 1.5 feet.

Multiple Choice

The function  $$P(c)=1.19c$$  represents the purchase price of candy bars at a gas station, where c represents the number of candy bars. If a customer has $10 to spend on candy bars, which is the most reasonable domain for this function?

• all real numbers where c ≥ 0

• all real numbers where c ≥ 10

• all whole numbers where 0 ≤ c ≤ 10

• all whole numbers where 0 ≤ c ≤ 8

Multiple Choice

The function  $$c(g)$$  can be used to represent the total cost, c, for g gallons of gas. What does  $$c(4)=12$$  represent?

• The total cost for 4 gallons of gas is $12.

• A customer buys 4 gallons of gas at a rate of $12 per gallon.

• A customer buys 12 gallons of gas at a rate of $4 per gallon.

• The total cost for 12 gallons of gas is $4.

Multiple Choice

The height, h, in feet, of a model rocket t seconds after being launched is modeled by the equation  $$h(t)=−16t^2+96t+10$$ .  The equation can be rewritten as  $$h(t)=−16(t−3)^2+154$$  .  

Which statement is revealed by rewriting the equation in this form? 

• The height from which the rocket is launched is 154 feet.

• The horizontal distance covered by the rocket is 3 feet.

• The maximum height attained by the rocket is 154 feet.

• The time after which the rocket lands on the ground is 3 seconds.

Multiple Choice

A student works for 80 hours each month and plans to work for 5 hours each day, but only on days when scheduled to work. The function  $$f(d)=80−5d$$  represents the number of hours of work remaining for the month after working for d days.

Which statement is true?

• The value of  $$f\left(4\right)$$  is 20, and it represents the number of hours of work remaining for the month after working for 4 days.

• The value of  $$f\left(4\right)$$  is 20, and it represents the number of hours spent working over 4 days.

• The value of  $$f\left(4\right)$$   is 60, and it represents the number of hours spent working over 4 days.

• The value of  $$f\left(4\right)$$  is 60, and it represents the number of hours of work remaining for the month after working for 4 days.

Multiple Choice

A gardener uses a riding lawn mower to mow a golf course. The gas tank of the lawn mower is half full when the gardener begins to mow. The function  $$g(n)=4−\frac{n}{2}$$  models the gallons of gas left in the tank after the gardener mows n acres.

What does 4 represent in the equation?

• the number of acres mowed after n minutes

• the number of gallons in the gas tank when the lawn mower starts
  

• the number of gallons the gas tank can hold total

• the number of total acres of the golf course
  

Multiple Choice

A gardener uses a riding lawn mower to mow a golf course. The gas tank of the lawn mower is half full when the gardener begins to mow. The function  $$g(n)=4−\frac{n}{2}$$  models the gallons of gas left in the tank after the gardener mows n acres.

How many gallons of gas will the gardener use to mow a single acre?

• 4 gallons

• 0.5 gallons

• 2 gallons

• 3.5 gallons

Multiple Choice

A gym charges a one-time fee for opening a gym membership in addition to a monthly fee for maintaining membership. The monthly fee is always the same amount, and the equation  $$T(m)=19.75m+10.00$$  represents the total cost of gym membership for mmm months. Which statement is true?

• The value 10.00 is the slope of the function, and it represents the amount of the one-time fee for opening a gym membership.

• The value 10.00 is the slope of the function, and it represents the monthly fee for maintaining the gym membership.

• The value 10.00 is the y-intercept of the function, and it represents the amount of the one-time fee for opening a gym membership.

• The value 10.00 is the y-intercept of the function, and it represents the monthly fee for maintaining the gym membership.

Multiple Choice

A school cafeteria has 210 bottles of orange juice. An orange juice company ships j boxes, each with 36 bottles of orange juice, to the school cafeteria.

Which statement is true?

• The total number of bottles of orange juice in the school cafeteria is best represented by a linear function because the number of bottles changes at a constant rate based on the value of j.

• The total number of bottles of orange juice in the school cafeteria is best represented by a linear function because the number of bottles does not change at a constant rate based on the value of j.

• The total number of bottles of orange juice in the school cafeteria is best represented by a nonlinear function because the number of bottles changes at a constant rate based on the value of j.

• The total number of bottles of orange juice in the school cafeteria is best represented by a nonlinear function because the number of bottles does not change at a constant rate based on the value of j.

Multiple Choice

A homeowner hires a carpenter for a project replacing kitchen cabinets. The homeowner pays a flat cost for materials and a price per hour, h, for the installation of the cabinets. The function  $$T(h)=35h+700$$  represents the total cost of the project. Which statement is true?

• The value 35 is the slope of the function, and it represents the flat cost for materials.

• The value 35 is the slope of the function, and it represents the price per hour for the installation of the cabinets.

• The value 35 is the y-intercept of the function, and it represents the flat cost for materials.

• The value 35 is the y-intercept of the function, and it represents the price per hour for the installation of the cabinets.