A sensor model starts as f(x) = x^2. A new calibration uses g(x) = 3(x - 4)^2 + 6. What output does the new model give when x = 10?
Reasoning strategy
Apply the horizontal shift inside the input, square, stretch, then shift the output.
Difficulty Practice Guide
Hard Grade 10 Function Transformations Word Problems
This page shows what hard practice should demand for grade 10 function transformations word problems. The goal is not a larger worksheet. The goal is to make the student's reasoning visible enough to choose the next better problem.
What Changes At This Difficulty
Stress-test transfer: multi-step structure, constraints, distractors, or reverse reasoning.
Expected structure: 3-4 step problem solving.
Vocabulary load: high with intentional distractors.
Reasoning depth: at least 3 relationship layers.
Student Work Signals
A good hard problem should expose the bottleneck
MathRoutine watches for whether the student understood the situation, wrote a useful setup, handled the calculation, and answered the exact question asked.
1
model hidden constraints or changed quantities
2
avoid tempting but incomplete first answers
3
explain why the final answer fits the original context
Sample Problems
A company models daily demand with f(x). A promotion shifts demand 2 days earlier and raises every output by 150 units. How should the transformed model be written?
Reasoning strategy
Represent an earlier input shift inside the function and the output increase outside.
Why This Matters
The paid value is diagnosis, not answer lookup
Basic gives repeated targeted practice. Pro becomes useful when the student needs help understanding wording, recovering the setup, or seeing the same misconception return across attempts.
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