Function Model Selection and Assumption Articulation - AP Precalculus
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What is assumed when using a logarithmic model?
What is assumed when using a logarithmic model?
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Logarithmic relationship. Data grows slowly then levels off asymptotically.
Logarithmic relationship. Data grows slowly then levels off asymptotically.
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Which function type is used for modeling depreciation?
Which function type is used for modeling depreciation?
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Exponential decay function. Value decreases by fixed percentage over time.
Exponential decay function. Value decreases by fixed percentage over time.
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What is the general form of a polynomial function?
What is the general form of a polynomial function?
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$f(x) = a_nx^n + a_{n-1}x^{n-1} + \ a_1x + a_0$. Sum of terms with non-negative integer powers.
$f(x) = a_nx^n + a_{n-1}x^{n-1} + \ a_1x + a_0$. Sum of terms with non-negative integer powers.
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What assumption is made for linear regression models?
What assumption is made for linear regression models?
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Linear relationship. Variables change at constant rate relative to each other.
Linear relationship. Variables change at constant rate relative to each other.
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Which function model describes logistic growth?
Which function model describes logistic growth?
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Logistic function. S-shaped curve with carrying capacity limit.
Logistic function. S-shaped curve with carrying capacity limit.
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What is the function type for a hyperbola?
What is the function type for a hyperbola?
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Rational function. Ratio of polynomials creates hyperbolic curves.
Rational function. Ratio of polynomials creates hyperbolic curves.
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Choose the function type for compound interest calculation.
Choose the function type for compound interest calculation.
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Exponential function. Interest compounds continuously over time.
Exponential function. Interest compounds continuously over time.
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What function type models constant rate of change?
What function type models constant rate of change?
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Linear function. Output changes by same amount per unit input.
Linear function. Output changes by same amount per unit input.
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Which function model is suitable for periodic data?
Which function model is suitable for periodic data?
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Trigonometric function. Repeats values in regular intervals.
Trigonometric function. Repeats values in regular intervals.
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Which function model is suitable for periodic data?
Which function model is suitable for periodic data?
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Trigonometric function. Repeats values in regular intervals.
Trigonometric function. Repeats values in regular intervals.
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Identify the function model for a bell curve.
Identify the function model for a bell curve.
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Normal distribution function. Gaussian distribution with characteristic bell shape.
Normal distribution function. Gaussian distribution with characteristic bell shape.
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Which function type is used for modeling elasticity?
Which function type is used for modeling elasticity?
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Logarithmic function. Percentage changes create logarithmic relationships.
Logarithmic function. Percentage changes create logarithmic relationships.
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What type of function is $f(x) = \text{sin}(x)$?
What type of function is $f(x) = \text{sin}(x)$?
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Trigonometric function. Basic sine function with period $2\pi$.
Trigonometric function. Basic sine function with period $2\pi$.
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Identify the function model for simple harmonic motion.
Identify the function model for simple harmonic motion.
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Trigonometric function. Sinusoidal oscillation about equilibrium position.
Trigonometric function. Sinusoidal oscillation about equilibrium position.
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What is the assumption for a power function model?
What is the assumption for a power function model?
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Power relationship. One variable proportional to power of another.
Power relationship. One variable proportional to power of another.
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Which function represents a constant function?
Which function represents a constant function?
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$f(x) = c$. Output value never changes regardless of input.
$f(x) = c$. Output value never changes regardless of input.
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Determine the function model for inverse variation.
Determine the function model for inverse variation.
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Rational function. One variable divided by another, form $y = \frac{k}{x}$.
Rational function. One variable divided by another, form $y = \frac{k}{x}$.
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What type of function is $f(x) = \frac{1}{x}$?
What type of function is $f(x) = \frac{1}{x}$?
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Rational function. Polynomial over polynomial with denominator $\neq 0$.
Rational function. Polynomial over polynomial with denominator $\neq 0$.
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What assumption is made in a trigonometric model?
What assumption is made in a trigonometric model?
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Periodicity. Pattern repeats at regular intervals.
Periodicity. Pattern repeats at regular intervals.
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What is the assumption for a quadratic model fit?
What is the assumption for a quadratic model fit?
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Parabolic relationship. Data follows U-shaped or inverted U pattern.
Parabolic relationship. Data follows U-shaped or inverted U pattern.
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What is the assumption for a power function model?
What is the assumption for a power function model?
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Power relationship. One variable proportional to power of another.
Power relationship. One variable proportional to power of another.
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Identify the function model for simple harmonic motion.
Identify the function model for simple harmonic motion.
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Trigonometric function. Sinusoidal oscillation about equilibrium position.
Trigonometric function. Sinusoidal oscillation about equilibrium position.
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What type of function is $f(x) = \text{sin}(x)$?
What type of function is $f(x) = \text{sin}(x)$?
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Trigonometric function. Basic sine function with period $2\pi$.
Trigonometric function. Basic sine function with period $2\pi$.
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Which function type is used for modeling elasticity?
Which function type is used for modeling elasticity?
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Logarithmic function. Percentage changes create logarithmic relationships.
Logarithmic function. Percentage changes create logarithmic relationships.
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What is the assumption for a normal distribution model?
What is the assumption for a normal distribution model?
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Symmetry and bell shape. Data clusters around mean in bell pattern.
Symmetry and bell shape. Data clusters around mean in bell pattern.
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Identify the function model for a bell curve.
Identify the function model for a bell curve.
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Normal distribution function. Gaussian distribution with characteristic bell shape.
Normal distribution function. Gaussian distribution with characteristic bell shape.
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What function type is used for quadratic regression?
What function type is used for quadratic regression?
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Quadratic function. Best-fit parabola through data points.
Quadratic function. Best-fit parabola through data points.
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Which function model describes bacterial growth?
Which function model describes bacterial growth?
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Exponential function. Reproduction rate proportional to current population.
Exponential function. Reproduction rate proportional to current population.
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What type of function is $f(x) = x^3 + 3x^2 + x + 1$?
What type of function is $f(x) = x^3 + 3x^2 + x + 1$?
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Cubic function. Highest power is 3, making it cubic.
Cubic function. Highest power is 3, making it cubic.
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Identify the assumption for a cubic model.
Identify the assumption for a cubic model.
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Cubic relationship. Data follows third-degree polynomial pattern.
Cubic relationship. Data follows third-degree polynomial pattern.
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