Algebra 2 | Unit 1 | Lesson 9: What’s the Equation? | Practice Problems

Complete this table showing the number of people \(P(n)\) who can sit at \(n\) tables. Describe how the number of people who can sit at the tables changes with each step. Explain why \(P(3.2)\) does not make sense in this scenario. Define \(P\) recursively and for the \(n^{\text{th}}\) term.

Tags

CCSS.HSF.IF.A.3

Complete the table with the height of the stack \(h(n)\), in mm, after \(n\) pennies have been added. Does \(h(1.52)\) make sense? Explain how you know.

Tags

CCSS.HSF.IF.A.2

Complete the table where \(A(n)\) is the area, in square inches, of the remaining paper after the \(n^{\rm th}\) person cuts off their fraction. Define \(A\) for the \(n^{\text{th}}\) term. What is a reasonable domain for the function \(A\)? Explain how you know.

Tags

CCSS.HSF.BF.A.2

List the first 5 terms of the sequence \(f(1)=35, f(n) = f(n-1) - 8\) for \(n\ge2\). Graph the value of each term as a function of the term number.

Tags

CCSS.HSF.BF.A.2

Here is a graph of sequence \(q\). Define \(q\) recursively using function notation.

Tags

CCSS.HSF.IF.A.3

Explain how you know that these definitions represent the same sequence: \(f(0) = 19, f(n) = f(n-1) - 6\) for \(n \geq 1\). The definition for the \(n^{\text{th}}\) term is \(f(n) = 19 - 6 \cdot n\) for \(n\ge0\). Select a definition to calculate \(f(20)\), and explain why you chose it.

Tags

CCSS.HSF.IF.A.3

An arithmetic sequence \(j\) starts 20, 16, . . . Explain how you would calculate the value of the 500th term.

Tags

CCSS.HSF.BF.A.2