Function Model Selection and Assumption Articulation - AP Precalculus

1. Identify the function type for projectile motion.

   Quadratic function. Gravity creates parabolic trajectory path.

2. What type of function is $f(x) = \frac{ax + b}{cx + d}$?

   Rational function. Linear numerator and denominator form rational function.

3. What type of function best models exponential growth?

   Exponential function. Growth rate is proportional to current value.

4. Which function model represents a straight line?

   Linear function. Constant slope creates straight-line graph.

5. What function type is used for quadratic regression?

   Quadratic function. Best-fit parabola through data points.

6. Which function type models a cubic relationship?

   Polynomial function. Highest degree term is 3, polynomial family.

7. Which function model describes logistic growth?

   Logistic function. S-shaped curve with carrying capacity limit.

8. Identify the assumption for exponential growth models.

   Constant growth rate. Multiplier remains same across time periods.

9. Which function model is suitable for periodic data?

   Trigonometric function. Repeats values in regular intervals.

10. What is the assumption for a quadratic model fit?

    Parabolic relationship. Data follows U-shaped or inverted U pattern.

11. Identify the function model for simple harmonic motion.

    Trigonometric function. Sinusoidal oscillation about equilibrium position.

12. Identify the function type for a parabolic graph.

    Quadratic function. U-shaped curve with vertex, has degree 2.

13. What type of function is $f(x) = \frac{1}{x}$?

    Rational function. Polynomial over polynomial with denominator $\neq 0$.

14. What is the general form of a logarithmic function?

    $f(x) = a \times \text{log}_b(x) + c$. Logarithm of variable with scaling constants.

15. Choose the function type for compound interest calculation.

    Exponential function. Interest compounds continuously over time.

16. What function type is $f(x) = a \times b^x$?

    Exponential function. Base raised to variable power creates exponential behavior.

17. Which function represents a constant function?

    $f(x) = c$. Output value never changes regardless of input.

18. Identify the assumption for a cubic model.

    Cubic relationship. Data follows third-degree polynomial pattern.

19. Which function type models harmonic motion?

    Trigonometric function. Oscillatory motion with sine/cosine patterns.

20. Which function type is used for modeling depreciation?

    Exponential decay function. Value decreases by fixed percentage over time.

21. Identify the function model for a bell curve.

    Normal distribution function. Gaussian distribution with characteristic bell shape.

22. What type of function is $f(x) = x^3 + 3x^2 + x + 1$?

    Cubic function. Highest power is 3, making it cubic.

23. What assumption is made for linear regression models?

    Linear relationship. Variables change at constant rate relative to each other.

24. What is the function type for a hyperbola?

    Rational function. Ratio of polynomials creates hyperbolic curves.

25. Determine the function type for a logarithmic scale.

    Logarithmic function. Inverse of exponential, grows slowly then levels.

26. What is the general form of a polynomial function?

    $f(x) = a_nx^n + a_{n-1}x^{n-1} + \\ a_1x + a_0$. Sum of terms with non-negative integer powers.

27. What is the assumption for a normal distribution model?

    Symmetry and bell shape. Data clusters around mean in bell pattern.

28. Determine the function model for inverse variation.

    Rational function. One variable divided by another, form $y = \frac{k}{x}$.

29. What is the assumption for a power function model?

    Power relationship. One variable proportional to power of another.

30. Which function type is used for modeling elasticity?

    Logarithmic function. Percentage changes create logarithmic relationships.

31. What function model is used for data with decay?

    Exponential decay function. Decreases by constant percentage each period.

32. What assumption is made in a trigonometric model?

    Periodicity. Pattern repeats at regular intervals.

33. Which function model describes bacterial growth?

    Exponential function. Reproduction rate proportional to current population.

34. What type of function is $f(x) = \text{sin}(x)$?

    Trigonometric function. Basic sine function with period $2\pi$.

35. What function type models constant rate of change?

    Linear function. Output changes by same amount per unit input.

36. Identify the function model for sinusoidal data.

    Trigonometric function. Sine and cosine waves repeat predictably.

37. What is assumed when using a logarithmic model?

    Logarithmic relationship. Data grows slowly then levels off asymptotically.

38. Determine the function model for damping oscillations.

    Exponential decay function. Amplitude decreases exponentially over time.

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