CC MATH 1021 1.11B LA
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Clemson University *
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1020
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Mathematics
Date
Apr 3, 2024
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MATH 1020 Calculus Concepts 1.11 Summary LA 1.11 Summary Section: ___ Group Number: _______
Score: ______/20 Name: _________________________________ Credit is only given for group work to those present on
all days LA is worked in class. 1. (7 pts) Complete the table by circling one answer in each cell. Question Linear Exponential Logarithmic Quadratic Logistic Cubic How many concavities can the function have? 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 Can the function ever change direction? Yes No Yes No Yes No Yes No Yes No Yes No How many horizontal asymptotes does the function have? 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 How many vertical asymptotes does the function have? 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 In the space below, sketch an example graph for each type of function. Make sure to label your graphs. O
O
&
oo
O
O
O
O
C
O
O
O
O
O
8
00
g
o
0
0
0
0
exponential
logarithmic
line
~
Cubic
quadratic
logistic
ru
~
MATH 1020 Calculus Concepts 1.11 Summary LA 1.11 Summary 2. (7 pts) Figure 1 Figure 2 Figure 3 Figure 4 Complete parts a-c
using the words: inflection point, relative max, relative min, limiting value a. The graph in Figure 1 shows a(n) ____________________, but the graph in Figure 3 does not. b. The graph in Figure 2 shows a(n) ____________________, but the graph in Figure 1 does not. c. The graph in Figure 4 shows a(n) ____________________, but the graph in Figure 2 does not. d. Based on the graphs above, determine which of the types of models we have talked about is represented in each figure. Figure 1: ____________________ Figure 2: ____________________ Figure 3: ____________________ Figure 4: ____________________ e. Recall that we can often determine which type of model is most appropriate for a data set based on the scatter plot. Suppose we get a scatter plot with the following behaviors and determine which model(s) is/are most appropriate. No curvature indicates a(n) ______________________ model. A single concavity indicates a(n) ____________________, ____________________, or _________________ model. An inflection point indicates a(n) ____________________ or ___________________ model. A limiting value indicates a(n) ____________________ or ___________________ model. f. Suppose that a scatter plot is concave down everywhere, has positive output values, and the input values range from x
= -1 to x
= 5. Which type of model would be most appropriate for this data? Explain why no other type of model is appropriate. relative
mil
inflection
put
limiting
val
quadratic
Cubic
exponential
logistic
linear
quadratic
exponential
logarithmic
Cubic
logistic
exponential
logistic
quadratic
one
concavity
positive
output
values
,
concave
down
negative
inpu
MATH 1020 Calculus Concepts 1.11 Summary LA 1.11 Summary 3. (6 pts) Remember that when deciding which model to use, it also helps to consider the expected function behavior based on the context. Consider the following data set: Input 1 2 3 4 5 6 Output 87.679 75.287 66.269 59.363 54.156 50.451 a. Use your calculator to view a scatterplot of the data. Based on what you see, which types of models could be appropriate for this data? If you fit the correct types of models, you should notice that they are all relatively good fits for the data. Then we need more information about the context of the problem to decide which model to use. b. Suppose that this data set is for the average high temperature in degree F each month in Clemson, SC during the school year, with an input value of 1 referring to August, 2 referring to September, etc. If we plan on using the model to predict temperatures during the school year (August to May), which type of model would be most appropriate and why? c. Suppose instead that this data set is for the sale price of a car in thousands of dollars, with the input giving the number of tens of thousands of miles the car has been driven. If we plan on using the model to extrapolate the sale price of the car to larger input values, which type of model would be most appropriate and why? d. Suppose instead that this data is for the temperature of an object placed in a very cold (well below 0 degrees F) environment, where the input gives the number of minutes that the object has been in the environment. If we plan on using the model to extrapolate the object’s temperature to longer exposure times, which type of model would be most appropriate and why? quadratic
,
exponential
,
logarithmic
quadratic
,
temps
expected
to
increase
again
exponential
,
value
expected
to
continue
toward
O
logarithmic
,
temp
expected
to
continue
to
decrease
into-values
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