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| Section | Objectives |
|---|---|
| Graphical Depictions | - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret concavity for situations - Interpret rates of change for situations |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Validity of Models | - Examine utility - Determine validity - Determine fit |
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
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NEW QUESTION # 128
A researcher collected data on the number of daily posts on a blog. The results are shown in the scatterplot.
The graphed regression function has an r
2
value of 0.89.
Is it appropriate to make a prediction for the number of daily posts after 18.6 months?
Answer: D
Explanation:
The value r2=0.89 indicates a strong fit because it is close to 1. A strong fit means the regression function follows the scatterplot data closely enough to support reasonable prediction. The question asks whether a prediction at x=18.6 months is appropriate. This value is outside the observed data range, so the prediction involves extrapolation. For a strong regression model, extrapolation can be acceptable if the new x-value is not too far beyond the maximum observed value. Here, x=18.6 is within 50% of the range beyond the maximum value, so the prediction is considered appropriate. Therefore, the correct answer is C.
NEW QUESTION # 129
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: A
Explanation:
To decide which town is growing faster, compare the slopes of the two lines. In a linear population graph, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A has a slope of about 1.0 thousand people per year, while Town B has a slope of about 0.7 thousand people per year. Since 1.0 > 0.7, Town A is growing at a faster rate. The values 6.5 and 5.5 refer to population amounts, not growth rates, so they do not answer the question. The correct comparison must use the slopes. Therefore, the correct answer is D.
NEW QUESTION # 130
The temperature of an object changes according to the relationship in the graph.
Which equation represents the horizontal asymptote of the function?
Answer: D
Explanation:
The graph shows the temperature of an object changing over time.
The horizontal axis represents:
" Time in minutes "
The vertical axis represents:
" Temperature in degrees Fahrenheit "
The curve is decreasing quickly at first and then begins to level off. This is the shape of an exponential decay function.
A horizontal asymptote is a horizontal line that the graph approaches as time increases.
Because a horizontal asymptote is a horizontal line, its equation must have the form:
y= " constant "
From the graph, the temperature approaches about:
25