Housing Prices The data in the table on the right represents the January median new-home prices in the United states for the years shown. ( a ) With a graphing utility, draw a scatter plot of the data. Comment on the type of relation that appears to exist between the two variables. ( b ) Decide on the function of best fit to these data ( linear, quadratic, or cubic ) , and use this function to predict the median new-phone price in the United States for January 2022 ( t = 10 ) . ( c ) Draw the function of best fit on the scatter plot obtained in part ( a ) .
Housing Prices The data in the table on the right represents the January median new-home prices in the United states for the years shown. ( a ) With a graphing utility, draw a scatter plot of the data. Comment on the type of relation that appears to exist between the two variables. ( b ) Decide on the function of best fit to these data ( linear, quadratic, or cubic ) , and use this function to predict the median new-phone price in the United States for January 2022 ( t = 10 ) . ( c ) Draw the function of best fit on the scatter plot obtained in part ( a ) .
Solution Summary: The author explains how to sketch the graph using graphing calculator using the steps below.
Housing Prices The data in the table on the right represents the January median new-home prices in the United states for the years shown.
(
a
)
With a graphing utility, draw a scatter plot of the data. Comment on the type of relation that appears to exist between the two variables.
(
b
)
Decide on the function of best fit to these data
(
linear, quadratic, or cubic
)
, and use this function to predict the median new-phone price in the United States for January
2022
(
t
=
10
)
.
(
c
)
Draw the function of best fit on the scatter plot obtained in part
(
a
)
.
Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.
2. Suppose the graph below left is the function f(x). In the space below, describe what
transformations are occuring in the transformed function 3ƒ(-2x) + 1. The graph it on the
coordinate plane below right. (4 points)
1
1. Suppose we have the function f(x) = = and then we transform it by moving it four units to the
right and six units down, reflecting it horizontally, and stretching vertically by 5 units. What will
the formula of our new function g(x) be? (2 points)
g(x) =
Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
(c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to
increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
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