DOK 3 Practice

Justify function comparisons and critique common reasoning errors.

These questions focus on choosing the best explanation, checking student claims, and comparing features across function families.

How to use this set

DOK 3 questions often ask for the best reason. Name the feature, then use evidence from the representation.

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Set Focus

Analysis and justification

Students need to explain why a function, comparison, or feature claim is valid.

Error analysis

Identify whether a claim uses the function rule correctly.

Feature comparison

Compare intercepts, maximums, minimums, and values.

Representation choice

Use the form that reveals the needed feature.

Long-term behavior

Compare linear and exponential growth for large inputs.

Practice Questions

Function Analysis and Error Correction

Check your answer first, then reveal the explanation when you want the model.

Question 1

Critique reasoning

A student says \{(1,4),(2,4),(3,4)\} is not a function because the output 4 repeats. What is the best response?

Question 2

Compare features

Function A is A(x)=2x+6. Function B is shown in the graph. Which statement is true?

Function B

Question 3

Reasonable domain

A function models the number of students left in a gym after m minutes. Why might the domain be restricted?

Question 4

Compare function families

Function A is linear and increases by 5 each step. Function B is exponential and doubles each step. Both start at 10. Which statement is most reasonable for large positive inputs?

Question 5

Error analysis

A student finds f(3) for f(x)=x^2+4 by doing 3^2+4=13. What should you say?

Question 6

Compare maximums

Function A has vertex (2,9) and opens downward. Function B has vertex (-1,7) and opens downward. Which statement is true?

Question 7

Representation choice

You need to find the zeros of q(x)=2(x-4)(x+1). Why is this form useful?

Question 8

Compare values

Function A is A(x)=x^2-2. Function B is B(x)=3x+2. Which function has the greater value at x=4?

Question 9

Correct comparison

Function A is A(x)=x^2-2. Function B is B(x)=3x+2. Which function has the greater value at x=5?

Question 10

Analyze table pattern

Which conclusion is best supported by the table?

Function values

x	y
0	2
1	5
2	10
3	17

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