A model f(x) = 3x^2 is shifted up 7 units to make g(x) = f(x) + 7. What is g(4)?
Reasoning strategy
Evaluate the original function first, then add the vertical shift.
Difficulty Practice Guide
Medium Grade 9 Function Transformations Word Problems
This page shows what medium practice should demand for grade 9 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
Add one meaningful reasoning layer so students must plan before calculating.
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 medium 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
separate useful numbers from background details
2
complete a two-step setup
3
interpret the result with the correct unit
Sample Problems
A model changes from f(x) = 2x^2 to g(x) = 2(x - 3)^2. What is g(8)?
Reasoning strategy
Change the input inside the parentheses before squaring.
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.
Compare plans