# 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
- C
- 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 m^{2}. 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.

**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.

- A
- B
- C
- D
- 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

**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?

- AAll the possible grades
- BStudents taking the test
- CTest scores
- DNonnegative numbers

What is the codomain of the function?

- ATest scores
- BAll the possible grades
- 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

**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

**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,

**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.

- A
- B
- C
- D
- E

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

- A
- B
- C
- D
- E

The outputs for inputs and are the same.

- A
- B
- C
- D
- E

**Q25: **

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

Input | 0 | 2 | 6 |
---|---|---|---|

Output | 0 | 6 | 18 |

- A
- B
- C
- D
- E