Seminar 3 – Worked Out Homework Option
8.1 #33.
Story problem
a. Write a set of four ordered pairs in which each of the least corrupt countries corresponds to a corruption rating. Each ordered pair should be in the form:
(country, corruption rating)
(Iceland, 9.7),(Finland,9.6),(New Zealand,9.6),(Denmark,9.5)
b. Is the relation in part (a) a function? Explain your answer.
It is a function because one input is inserted (country) and an output is given (corruption rating)
c. Write a set of four ordered pairs in which corruption ratings for the least corrupt countries correspond to countries. Each ordered pair should be in the form:
(corruption rating, country)
(9.7, Iceland),(9.6,Finland),(9.6,New Zealand),(9.5,Denmark)
d. Is the relation in part (c) a function? Explain your answer.
This is not a function because the output is falsely given as the dependent variable. It may be the inverse, but not a function. The rating is dependent upon the country, not the other way around.
8.2 #55.
Story problem
The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces, for weights not exceeding 3.5 ounces. Use the graph to solve.
Find f(3). What does this mean in terms of the variables in this situation?
f(3) = 0.75
that means anything between any more than 2oz up to 3oz is 0.75
8.3 #63.
Story problem.
a. Write a function that models the total US population for the years shown in the bar graph.
Take the midpoints of all values:
T(x) = 3.01(x) + 235.3 (I added male + female in the calculation)
b. Use the function from part (a) to find the total US population in 2005.
3.01(20) + 235.3 = 295.5 million people
c. Does the result in part (b) overestimate or underestimate the actual total US population in 2005 shown by the bar graph? By how much?
2005 total = 147 + 151 = 298 – 295.5 = 2.5million under-estimation.
8.4 #67.
The formula
y=fx=95x+32
is used to convert from x degrees Celsius to y degrees Fahrenheit. The formula
y=gx=59(x-32)
is used to convert from x degrees Fahrenheit to y degrees Celsius. Show that f and g are inverse functions.
Swap x and y
y=59x-32
x=59y-32
x(95)=(95)59y-32
x95=y-32
x95+32=y-32+32
x95+32=y =y=fx=95x+32…PROVED
8.5 (-∞, 5) can be rewritten (5,∞).why are they equal
They are inverse of each other. The plotted point on the graph would have to turned clockwise one quarter to get the result of the second point.