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Algebra 1

4.4.3 Using Tables to Find Function Rules

Algebra 14.4.3 Using Tables to Find Function Rules

4.4.3 Using Tables to Find Function Rules

4.4.3 • Using Tables to Find Function Rules

Activity

1. A square that has a side length of 9 cm has an area of 81 c m 2 c m 2 . The relationship between the side length and the area of the square is a function.

For questions a-e use the table by answering each question.

a. What is the area in c m 2 c m 2 when the side length is 1cm 1cm ?

b. What is the area in c m 2 c m 2 when the side length is 2cm 2cm ?

c. What is the area in c m 2 c m 2 when the side length is 4cm 4cm ?

d. What is the area in c m 2 c m 2 when the side length is 6cm 6cm ?

e. Write a rule for a function, A A , that gives the area of the square in c m 2 c m 2 when the side length is s s c m c m .

f. What does A ( 2 ) A ( 2 ) represent in this situation? What is its value? Write your answers, then click solution to compare your answer.

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g. Sketch a graph of this function. Use the desmos graphing tool or technology outside the course.

2. A roll of paper that is 3 feet wide can be cut to any length.

a. If we cut a length of 2.5 feet, what is the perimeter of the paper? Enter your answer in feet.Use integers only.

For questions b-f, keep in mind that the roll of paper is 3 feet wide. Complete the table by answering each question.

side length (feet) perimeter (feet)

1

 b. _______

2

 c. _______

6.3

 d. _______

11

 f. _______

b. If we cut a length of 1 foot, what is the perimeter of the paper to the nearest whole foot?

c. To the nearest whole foot, what is the perimeter when the side length is 2 feet?

d. What is the exact perimeter, in feet, when the side length is 6.3 feet?

e. What is the perimeter, to the nearest whole foot,when the side length is 11 feet?

f. Write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is l.

g. What does P(11) represent in this situation? What is its value?

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h. Sketch a graph of this function. Use the desmos graphing tool or technology outside the course.

Video: Writing Function Rules

Watch the following video to learn more about writing rules with function notation.

Writing Function Rules

Self Check

Which function rule can describe the table below?

x y

1

3

2

5

5

11
  1. f ( x ) = x + 2
  2. f ( x ) = 2 x + 2
  3. f ( x ) = 2 x + 1
  4. f ( x ) = x + 3

Additional Resources

Write the Function Rule from a Table

Kelly can tune 6 cars in 3 hours. The table below is completed to show this relationship. The last column has the output for any x x . This is the rule of the function.

Kelly can tune 6 cars in 3 hours or 2 cars in 1 hour, so the function rule is f ( x ) = 2 x f ( x ) = 2 x .

Try it

Write the Function Rule from a Table

Determine the rule in function notation for the table below:

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