Use this free practice quiz with 20 questions to review Modeling Functions and Data, test your knowledge, and prepare for your next test or exam.
A scatter plot of delivery distance versus delivery cost shows points clustered around a straight line with an approximately constant increase in cost for each additional mile. Which function family is the most appropriate initial model?
A trigonometric model
A linear model
A rational model
A logarithmic model
For the polynomial model f(x)=−3x4+2x3+7, which statement correctly identifies two of its features?
The degree is 3, and the leading coefficient is 7.
The degree is 7, and the leading coefficient is 4.
The degree is 4, and the leading coefficient is −3.
The degree is −3, and the leading coefficient is 4.
An amount is modeled by A(t)=500(0.92)t. What does the factor 0.92 represent?
The quantity decreases by 8% per time unit.
The quantity decreases by 92% per time unit.
The quantity increases by 8% per time unit.
The quantity increases by 92% per time unit.
What is the period of the model f(t)=6sin(4πt−2)+10, assuming the angle is measured in radians?
4π units
2π units
4 units
8 units
Which two practices are appropriate when assessing whether a function model is defensible for a real situation? Select all correct choices.
Check whether the model's domain and range are meaningful in context.
Choose the model with the highest R2 without further analysis.
Inspect residuals for systematic patterns.
Use the most complicated function available to ensure accuracy.
Assume interpolation and extrapolation are equally reliable.
A temperature model has a maximum of 30∘C, a minimum of 10∘C, and reaches a corresponding maximum every 24 hours. Which two statements are correct? Select all correct choices.
The amplitude is 20 and the midline is 10.
The amplitude is 10 and the midline is 20.
The period is 12 hours and the midline is 20.
The period is 24 hours and the amplitude is 10.
The amplitude is 40 and the period is 24 hours.
True or false: A function model is an approximation that can describe a pattern and support predictions, rather than a claim that real data follow an equation perfectly.
True
False
True or false: Predictions made outside the range of observed input values are generally safer than predictions made within that range.
True
False
What is the statistical term for the difference between an observed response value and its model-predicted value?
Observed values are 2, 4, and 6, while the corresponding model predictions are 1, 7, and 5. What is the root mean square error (RMSE), rounded to two decimal places?
A function uses different formulas on different intervals when a pricing rule changes at a .
In a rational function, the identifies input values at which the function is .
Explain how a residual plot can be used to judge whether a selected function family is appropriate. Describe the pattern that generally supports the model and explain what at least two nonrandom residual patterns might indicate.
A learning study shows that performance improves quickly during the first few practice sessions, then the gains become progressively smaller. Which model is a defensible initial choice, assuming the input satisfies the model's domain restriction?
A linear model, because all increasing data are linear
A polynomial model of arbitrarily high degree, because it can pass through many points
A logarithmic model, because the change is rapid initially and then gradually levels off
A trigonometric model, because every increasing sequence is periodic
What is the primary purpose of a function model?
It guarantees that every observed value will lie exactly on the equation.
It approximates a relationship so that patterns can be described and values can be predicted.
It eliminates the need to identify the variables and their units.
It applies only when the data are perfectly periodic.
A data set shows that each one-unit increase in the input multiplies the output by approximately the same factor. Which function family is the most appropriate initial choice?
A linear model
A polynomial model
An exponential model
A piecewise model
In a polynomial model, what does the degree represent?
The highest power of the input variable
The coefficient of the constant term
The number of zeros shown by the graph
The value of the model when the input is zero
True or false: A high R2 value by itself guarantees that a model is appropriate for the context.
True
False
A periodic temperature has a maximum of 26∘C and a minimum of 10∘C. What is the amplitude of the model? Enter the numeric value in degrees Celsius.
What term describes using a model to predict an output for an input value within the range of observed inputs?