AP PreCalculus Practice Quiz: Function Model Selection and Assumption Articulation
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 16 questions to check your progress.
Question 1 of 16
All Questions (16)
A) Quadratic
B) Linear
C) Cubic
D) Piecewise-defined
Correct Answer: B
The cost increases by a constant amount ($0.50) for each additional mile. According to the content, linear functions are appropriate for scenarios that demonstrate a roughly constant rate of change.
A) Linear, because the acceleration is constant.
B) Quadratic, because the rate of change of distance (speed) is changing linearly.
C) Cubic, because it involves a three-dimensional scenario.
D) Piecewise-defined, because the object starts at rest and then falls.
Correct Answer: B
The rate of change of the distance is the speed, which is increasing at a constant rate (9.8 m/s per second). This means the speed is changing linearly. The content states that quadratic functions model scenarios that demonstrate roughly linear rates of change.
A) Linear
B) Cubic
C) Quadratic
D) Piecewise-defined
Correct Answer: C
The area of a square is calculated by squaring its side length (Area = side^2). The content specifies that geometric contexts involving area or two dimensions can often be modeled by quadratic functions.
A) Linear
B) Quadratic
C) Cubic
D) Piecewise-defined
Correct Answer: D
The scenario has two different rules for calculating the cost based on the amount of data used (one rule for 0-5 GB, and another for >5 GB). The content states that a piecewise-defined function is useful for modeling a scenario that demonstrates different characteristics over different intervals.
A) t > 2020
B) 0 ≤ t ≤ 10
C) M(t) ≥ 0
D) All real numbers
Correct Answer: B
The domain represents the input values (time in years). The model starts in 2020 (t=0) and is used for a decade (10 years). Therefore, the time t must be between 0 and 10, inclusive. This is a domain restriction based on contextual clues.
A) Linear
B) Quadratic
C) Cubic
D) Piecewise-defined
Correct Answer: C
The volume of a sphere is (4/3)πr³. Since the model relates the radius to the volume, it involves three dimensions. The content states that geometric contexts involving volume or three dimensions can often be modeled by cubic functions.
A) The domain must be x ≥ 0.
B) The domain must consist of non-negative integers.
C) The output values P(x) must be rounded to the nearest integer.
D) The output values P(x) must be rounded to two decimal places.
Correct Answer: D
Profit is a monetary value, which is typically represented in dollars and cents. A range restriction based on this contextual clue would require rounding the output values to two decimal places. Options A and B describe domain restrictions, not range restrictions.
A) The rate of change is accelerating.
B) The rate of change is different over different intervals.
C) The rate of change is roughly constant.
D) The data involves a geometric area.
Correct Answer: C
The provided content explicitly states that 'Linear functions model data sets or aspects of contextual scenarios that demonstrate roughly constant rates of change.' This is the fundamental assumption when applying a linear model.
A) The total distance traveled by a car moving at a constant speed of 60 mph.
B) The total earnings of a worker who makes $20 per hour.
C) The area of a rectangular field with a fixed length and a variable width.
D) The height of a ball thrown upwards, as a function of time.
Correct Answer: D
The height of a thrown ball is affected by gravity, which causes its upward velocity to decrease linearly until it becomes negative. Since the rate of change (velocity) is linear, the function for position (height) is quadratic.
A) x must be greater than 0.
B) x cannot be equal to 5.
C) x must be an integer.
D) x cannot be equal to 0.
Correct Answer: B
The expression 1/(x-5) is undefined when the denominator is zero. The denominator is zero when x - 5 = 0, or x = 5. This is a domain restriction based on a mathematical clue (division by zero).
A) Assumption: Cars can be fractions. Range: All positive real numbers.
B) Assumption: The number of levels can be negative. Range: All real numbers.
C) Assumption: The number of cars must be a whole number. Range: The output values must be rounded to the nearest non-negative integer.
D) Assumption: The rate of change is constant. Range: The output must be rounded to two decimal places.
Correct Answer: C
Contextually, you cannot have a fraction of a car. This is a fundamental assumption. Therefore, the range of the function, which represents the number of cars, must be restricted to non-negative integers. This may require rounding the values produced by the model.
A) Because the shipping cost has a constant rate of change for all package weights.
B) Because the shipping cost changes based on a linear rate of change.
C) Because the rules for calculating the cost are different for different weight brackets.
D) Because the cost is related to the volume of the package.
Correct Answer: C
Piecewise-defined functions are used when a scenario demonstrates different characteristics over different intervals. In this case, the 'intervals' are the different weight brackets, each with its own pricing rule.
A) The population is exactly 345.78; this is a domain restriction.
B) The population is approximately 346; this is a range restriction requiring rounding.
C) The model is invalid because the output is not an integer; this is a model selection error.
D) The population is approximately 345.78; this is an assumption about constant growth.
Correct Answer: B
The population of a species must be a whole number. A model outputting a decimal value must be interpreted in context. This requires a range restriction, where the output values are rounded to the nearest integer to be meaningful.
A) Linear, because the height is constant.
B) Quadratic, because the volume formula involves the radius squared.
C) Cubic, because volume is a three-dimensional property.
D) Piecewise-defined, because the radius must be positive.
Correct Answer: B
The volume of a cylinder is V = πr²h. Since the height (h) is fixed, the volume is a constant multiple of r². This relationship between volume and radius is quadratic. This is a geometric context involving an area (the circular base) scaled by a constant height, leading to a quadratic model with respect to the radius.
A) The model should have been cubic, not linear.
B) The prediction is outside the domain of the original data set, which is a contextual restriction.
C) The prediction is outside the range of extreme values in the original data set, suggesting the model may not be accurate for that input.
D) The model did not properly round the output, which is a required range restriction.
Correct Answer: C
Models are generally most reliable within the range of the data used to create them. A prediction of $50,000 is an extreme value, far below the minimum of the data set ($150,000). The content notes that a model may require domain or range restrictions based on extreme values in the data set, and extrapolating far beyond these values can lead to unreliable results.
A) A contextual clue, such as time cannot be negative.
B) A mathematical clue, such as avoiding division by zero.
C) An extreme value from the data set used to build the model.
D) A requirement that the output of the function must be an integer.
Correct Answer: D
The requirement that the output must be an integer is a range restriction, as it concerns the possible output values of the function. Domain restrictions, according to the content, are based on mathematical clues, contextual clues, or extreme values in the input data set.