The function f ( x ) = 2.9 x + 20.1 models the median height, f(x), in inches, of boys who are x months of age. The graph of is shown. a. Describe how the graph can be obtained using transformations of the square root function f ( x ) = x . b. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height? c. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. d. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (c)? How is this difference shown by the graph?
The function f ( x ) = 2.9 x + 20.1 models the median height, f(x), in inches, of boys who are x months of age. The graph of is shown. a. Describe how the graph can be obtained using transformations of the square root function f ( x ) = x . b. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height? c. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. d. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (c)? How is this difference shown by the graph?
Solution Summary: The author explains the steps of obtaining the graph of the function f(x)=2.9sqrtx+20.1 using transformation.
The function
f
(
x
)
=
2.9
x
+
20.1
models the median height, f(x), in inches, of boys who are x months of age. The graph of is shown.
a. Describe how the graph can be obtained using transformations of the square root function
f
(
x
)
=
x
.
b. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height?
c. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth.
d. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (c)? How is this difference shown by the graph?
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A falling object travels a distance given by the formula d = 6t + 9t2 where d is in feet
and t is the time in seconds. How many seconds will it take for the object to travel
112 feet? Round answer to 2 decimal places. (Write the number, not the units).
Your Answer:
Solve by the quadratic formula or completing the square to obtain exact solutions.
2
e
104
OA) -16±3√6
B) 8±√10
O c) -8±√10
OD) 8±3√√6
U
Question 14 (1 point)
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The frame on a picture is 18 in by 22 in outside and is of uniform width. Using
algebraic methods, what is the width of the frame if the inner area of the picture
shown is 250 in²2? Write answer to 2 decimal places. (Write the number with no
units).
18 in
Your Answer:
22 in
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