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Grade 8 · unit review

Review: Functions, Nonlinear Patterns, and Domains

A function assigns one output to each allowed input. A table can reveal nonlinear structure or interval-average change, while the domain records which inputs make sense mathematically and in the supplied context.

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Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. Among the supplied sets using inputs 7, 8 and 9, which defines y as a function of x?
Need a hint?
  • Repeated outputs are permitted in a function, but a repeated input cannot be paired with two different outputs.
  • The rule concerns one output per input, not one input per output.
2. At x=0,1,2,3 a rule has outputs 0,7,28,63. Which formula matches all four?
Need a hint?
  • A quadratic table can arise by multiplying squared inputs by a constant.
  • Matching just one point cannot identify a rule.
3. A function has f(2)=7 and f(4)=28. What is its average rate of change from x=2 to x=4?
Need a hint?
  • Average rate of change measures the net output change per net input change between two endpoints.
  • Keep subtraction order consistent in numerator and denominator.
4. A fictional box holds at most 12 whole markers. The input counts how many markers are in it. Which domain fits?
Need a hint?
  • A counting context supplies input restrictions beyond a formula.
  • Do not include fractions just because an algebraic formula can evaluate them.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. Among the supplied sets using inputs 9, 10 and 11, which defines y as a function of x? Candidate answers: (A) (10,0), (10,1), (11,2) (B) (11,2), (11,3), (9,1) (C) (9,1), (10,1), (11,2) (D) (9,1), (9,2), (10,3). 2. At x=0,1,2,3 a rule has outputs 0,9,36,81. Which formula matches all four? Candidate answers: (A) y=9x (B) y=9x² (C) y=9x³ (D) y=x+9. 3. A function has f(2)=9 and f(4)=36. What is its average rate of change from x=2 to x=4? Candidate answers: (A) 12.5 (B) 14.5 (C) 27 (D) 27/2. 4. A fictional box holds at most 14 whole markers. The input counts how many markers are in it. Which domain fits? Candidate answers: (A) All positive real numbers (B) All real numbers from 0 to 14 (C) Integers 0 through 14 (D) Integers greater than 14.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. (9,1), (10,1), (11,2). The correct set assigns each of the three distinct inputs 9, 10 and 11 exactly one output. Repeated output 1 is allowed; one input with two outputs is not. 2. y=9x². The values are 9 times 0²,1²,2²,3². First differences are 9,27,45, not constant; this is not a linear rule. 3. 27/2. Use change in output divided by change in input: (36−9)/(4−2)=27/2=27/2. This is the interval average; it need not hold at every point. 4. Integers 0 through 14. You cannot have a fractional marker in this counting model, and an empty box is possible. The capacity makes 14 the largest allowed input.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.