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The student cannot write a function rule for arithmetic and geometric sequences. Examples of Student Work at this Level The student may observe common differences and common ratios in successive terms but is unable to write function rules that can be used to generate the terms of the sequences.

Questions Eliciting Thinking I see that you found a common difference of four for the first sequence. What does that tell you about the type of sequence? What kind of function describes this type of sequence? I see that you found a common ratio of two for the second sequence.

Instructional Implications Assist the student in identifying a sequence as arithmetic by observing a common difference between pairs of successive terms. Explain that function rules for arithmetic sequences are linear functions. Assist the student in applying methods for writing linear functions given two ordered pair solutions to writing function rules for arithmetic sequences.

After providing additional examples, guide the student to observe the relationship between the common difference and the coefficient of the term number, n, in the function rule.

Assist the student in identifying a sequence as geometric by observing a common ratio between pairs of successive terms. Explain that function rules for geometric sequences are exponential functions. Assist the student in applying methods for writing exponential functions given two ordered pair solutions to writing function rules for geometric sequences.

After providing additional examples, guide the student to observe the relationship between the common ratio and the base of the exponential factor in the function rule. Provide additional examples of arithmetic and geometric sequences and ask the student to write function rules.

Moving Forward The student is only able to write a linear function to represent the arithmetic sequence. Examples of Student Work at this Level The student correctly writes a linear function to represent the arithmetic sequence, but is not able to correctly write an exponential function to represent the geometric sequence.

Questions Eliciting Thinking Is the second sequence arithmetic? Why or why not? What do you know about the second sequence? Instructional Implications Assist the student in identifying a sequence as geometric by observing a common ratio between pairs of successive terms.

If needed, assist the student in developing algebraic strategies rather than trial and error for writing function rules for arithmetic sequences. Almost There The student makes a minor error.

Examples of Student Work at this Level The student correctly writes each function but: Questions Eliciting Thinking Is the notation you used consistent with the notation given in the problem?

What problems might arise from introducing new notation in your work and answer? What kind of sequence is the second sequence?

When working with geometric sequences, what is the name for the factor by which one term can be multiplied to get the next term? Instructional Implications If the student referred to the common ratio as the growth factor, commend him or her on observing the relationship between geometric sequences and exponential functions.

Remind the student of the terminology used in the context of sequences e. If needed, assist the student in developing algebraic strategies for writing function rules rather than using trial and error.

Got It The student provides complete and correct responses to all components of the task. What kind of function can be written for an arithmetic sequence?

What kind of function can be written for a geometric sequence? Instructional Implications Challenge the student to write a function rule for a sequence represented by a quadratic function such as 2, 6, 12, 20, 30….

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Find The Function Rule. Showing top 8 worksheets in the category - Find The Function Rule. Some of the worksheets displayed are Tables and function rule quiz review, Functions as patterns, Math 1a calculus work, Functionswork, Arithmetic sequences date period, Name score, Determine the equation 2 variables, Name date ms.

Lesson “ Writing a Function Rule Model the function rule with a table of values. 1. f(x) = 5x - 1 Key Concept Writing Function Rules Examples Writing a Function Rule from a Table Directions: Write a function rule for each table.

1. . Writing a Function Rule 9th - 11th In this Algebra I/Algebra II worksheet, students determine the equation that correctly represents the relationship between the x and y values provided.

Demystifies function notation, specifying that the parentheses do not indicate multiplication, and demonstrates how to evaluate a function at a number.

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