# Worksheet: Forming Functions

In this worksheet, we will practice forming and deriving the equation of a function from different situations.

Q1:

Find an expression for the area of a square as a function of its diagonal length .

• A
• B
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• D
• E

Q2:

A raindrop hitting a lake makes a circular ripple. The radius, in inches, grows as a function of time, in minutes, according to . Find the area of the ripple as a function of time, and then determine the area of the ripple at 3 seconds.

• A inches, square inches
• B inches, square inches
• C inches, square inches
• D inches, square inches
• E inches, square inches

Q3:

A rectangular piece of land has a length m and an area of 2,775 m2. Find a function to calculate the width and find the width when the length is 75 m.

• AThe function and the width is 18.5 m.
• BThe function and the width is 208,125 m.
• CThe function and the width is 2,700 m.
• DThe function and the width is 37 m.

Q4:

The volume of a cylinder can be described by the function . Find a formula to describe the volume of a cylinder where the radius is three times the height.

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• B
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• D

Q5:

The radius of a circular oil slick is expanding at a rate of 20 meters per day. Express the area of the circle as a function of , the number of days elapsed.

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• E

Q6:

The number of honey jars, , produced by a swarm of bees, ,is given by . A particular forest has 3 swarms of bees that produced 12 jars of honey. Express this information in terms of the function .

• A
• B
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• D

Q7:

An oil spill grows with time such that its boundary is always a circle. Suppose that the radius is given by as a function of time . Express the area of the spill as a function of time.

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• E

Q8:

The number of cubic yards of dirt, , needed to cover a garden whose area is square feet is given by . A garden with area 5,000 ft2 requires 50 yd3 of dirt. Express this information in terms of the function .

• A
• B
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• D
• E

Q9:

A rectangle has a length of 10 units and a width of 8 units. Squares of by units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of .

• A
• B
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• E

Q10:

A gardener has 200 feet of fencing which he can use to enclose an area for a rectangular garden. By putting the garden against one wall of the house, only three sides need to be fenced. Let be the length of the side perpendicular to the wall of the house. Write a function in terms of for the area of the resulting garden.

• A
• B
• C
• D

Q11:

The amount of garbage produced by a town with a population is given by . is measured in tons per week, and is measured in thousands of people. Suppose a town has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function .

• A
• B
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• E

Q12:

Assigning test grades to students is an example of a function.

Which of the following is this function written in function notation?

• A(grade of student A on the test) = student A
• B(student A) = grade of student A on the test

What is the domain of the function?

• BStudents taking the test
• CTest scores
• DNonnegative numbers

What is the codomain of the function?

• ATest scores
• CStudents taking the test
• DNonnegative numbers

Q13:

If the input of the function is , then the output of the function is .

• A
• B
• C
• D

Q14:

Which of the following is equation expressed as a function of .

• A
• B
• CThis cannot be expressed as a function of .
• D
• E

Q15:

A rectangle has a length of 10 inches and a width of 6 inches. If the length is increased by inches and the width is increased by twice that amount, express the area of the rectangle as a function of .

• A
• B
• C
• D
• E

Q16:

The volume of mercury in a particular thermometer is a function of the measured temperature . If the temperature is the input and the volume is the output of this function, does each unique temperature give rise to a specific volume?

• Ano
• Byes

Q17:

A square has sides of length 12. Squares measuring by are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a function in terms of .

• A
• B
• C
• D
• E

Q18:

Given that is the area of a circle, and is its radius, express as a function of , and determine the value of giving your answer in terms of if necessary.

• A,
• B,
• C,
• D,
• E,

Q19:

A rectangle is twice as long as it is wide. Squares of length 2 units are cut out from each corner. Then, the sides are folded up to make an open box. Express the volume of the box as a function of the width .

• A
• B
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• D
• E

Q20:

A rectangle has a perimeter of 36. Find a function to describe the area of the rectangle, based upon its width.

• A
• B
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• D

Q21:

A cube is increasing in size. Initially, an edge measured 3 feet, and it increases at a rate of 2 feet per minute. Find an expression for the volume of the cube, , as a function of the number of minutes elapsed, . Write your answer as a polynomial in standard form.

• A
• B
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• E

Q22:

Rewrite the following in terms of a function , using the language of inputs and outputs.

The output is greater than 5 when the input is 7.

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• E

The output at input is the same as the sum of the outputs at and .

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• E

The outputs for inputs and are the same.

• A
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• E

Q23:

A right circular cone has a radius of and its height is 3 units less than its radius. Express the volume of the cone as a polynomial function, knowing that the volume of a cone with radius and height is .

• A
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• D
• E

Q24:

A portion of fencing 100 feet long is cut into two pieces. One piece, which is feet long, is used to enclose a square pen. The other piece is shaped into an enclosure as an equilateral triangle. What is the total area enclosed as a function of ?

• A
• B
• C
• D

Q25:

Write an equation that describes the relationship between the input and output.

 Input (๐ฅ) Output (๐ฆ) 0 2 6 0 6 18
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• E