Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
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For f(x)=2x²−3 and x=3, evaluate f(x).
2. {'id': 'u01-l06', 'number': 6, 'title': 'Inverse Functions and Restricted Domains', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
State the domain of g(x)=√(x−4).
3. {'id': 'u01-l06', 'number': 6, 'title': 'Inverse Functions and Restricted Domains', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
Find the average rate of change of f(x)=x² from x=1 to x=4.
4. {'id': 'u01-l06', 'number': 6, 'title': 'Inverse Functions and Restricted Domains', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
Describe the transformation from y=x² to y=−2(x−3)²+1.
5. {'id': 'u01-l06', 'number': 6, 'title': 'Inverse Functions and Restricted Domains', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
If f(x)=x+2 and g(x)=3x, find (f∘g)(4).
6. {'id': 'u01-l06', 'number': 6, 'title': 'Inverse Functions and Restricted Domains', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
Find the inverse of f(x)=5x−7.
7. {'id': 'u01-l07', 'number': 7, 'title': 'Choosing, Fitting & Validating Models', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
For f(x)=2x²−3 and x=4, evaluate f(x).
8. {'id': 'u01-l07', 'number': 7, 'title': 'Choosing, Fitting & Validating Models', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
State the domain of g(x)=√(x−4).
9. {'id': 'u01-l07', 'number': 7, 'title': 'Choosing, Fitting & Validating Models', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
Find the average rate of change of f(x)=x² from x=1 to x=4.
10. {'id': 'u01-l07', 'number': 7, 'title': 'Choosing, Fitting & Validating Models', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
Describe the transformation from y=x² to y=−2(x−3)²+1.
11. {'id': 'u01-l07', 'number': 7, 'title': 'Choosing, Fitting & Validating Models', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
If f(x)=x+2 and g(x)=3x, find (f∘g)(4).
12. {'id': 'u01-l07', 'number': 7, 'title': 'Choosing, Fitting & Validating Models', 'family': 'functions', 'week': 3, 'unit': 1, 'unit_title': 'Advanced Function Language, Representations & Modelling', 'essential': 'How do domain, range, rate of change, composition, inverse structure, and multiple representations reveal what a function can model?', 'project': 'Function Atlas & Model Selection Defense'}
Find the inverse of f(x)=5x−7.