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IM: 8.5.3: Equations for Functions (Lesson)

Last updated 9 months ago
10 questions
3.1: A Square’s Area
1

Fill in the table of input-output pairs for the given rule.

1

Write an algebraic expression for the rule in the box in the diagram.

3.2: Diagrams, Equations, and Descriptions
1

Record your answers to these questions in the table provided.
  1. Match each of these descriptions with a diagram:
a. the circumference, C, of a circle with radius, r b. the distance in miles, d, that you would travel in t hours if you drive at 60 miles per hour c. the output when you triple the input and subtract 4 d. the volume of a cube, v given its edge length, s
2. Write an equation for each description that expresses the output as a function of the input.

3. Find the output when the input is 5 for each equation.

4. Name the independent and dependent variables of each equation.

Are you ready for more?
1

Choose a 3-digit number as an input.

Apply the following rule to it, one step at a time:
  • Multiply your number by 7.
  • Add one to the result.
  • Multiply the result by 11.
  • Subtract 5 from the result.
  • Multiply the result by 13
  • Subtract 78 from the result to get the output.
Can you describe a simpler way to describe this rule? Why does this work?

3.3: Dimes and Quarters
Jada had some dimes and quarters that had a total value of $12.50. The relationship between the number of dimes, d, and the number of quarters, q, can be expressed by the equation 0.1d + 0.25q = 12.5.
1

If Jada has 4 quarters, how many dimes does she have?

1

If Jada has 10 quarters, how many dimes does she have?

1

Is the number of dimes a function of the number of quarters? If yes, write a rule (that starts with d =...) that you can use to determine the output, d, from a given input, q. If no, explain why not.

1

If Jada has 25 dimes, how many quarters does she have?

1

If Jada has 30 dimes, how many quarters does she have?

1

Is the number of quarters a function of the number of dimes? If yes, write a rule (that starts with q =...) that you can use to determine the output, q, from a given input, d. If no, explain why not.