Write a function that models the total population for the

Question

1. Use the graph of the function to identify its domain and its range.

a. Select the correct choice below and fill in the answer box to complete your choice.

A. The domain contains infinitely many points. The domain in interval notation is_.

B. The domain can be described by a list of distinct numbers. The domain is {x|x = (Use a comma to separate answers as needed.)

b. Select the correct choice below and fill in the answer box to complete your choice.

A. The range contains infinitely many points. The range in interval notation is__.

B. The range can be described by a list of distinct numbers. The range is {y|y = __}. (Use a comma to separate answers as needed )

2. The bar graph shows the population of a particular country. in millions. for five selected years. The two following functions model the data. where x is the number of years after 1985.

M(x)= 1.91x + 117.4     male population
F(x)= 1.79x + 141.2     female population

Answer the following questions.

a. Write a function that models the total population for the years shown in the bar graph.

Choose the correct answer below.

A. (M +F)(x) = 3.7x + 258.6

B. (M/F)(x)= 1.067x - 0.83

C. (MF)(x) = 3.419x + 16576.88

D. (M - F)(x)= 0.12x - 23.8

b. Use the function from part (a) to find the total population in 2005.

The total population in 2005 was __ million. (Round to one decimal place as needed.)

c. Does the result in part (b) overestimate or underestimate the actual total population in 2005 shown by the bar graph? By how much?

Choose the correct answer below.

The result in part (b) underestimates the actual total population in 2005 shown by the bar graph by 4.6 million.

The result in part (b) overestimates the actual total population in 2005 shown by the bar graph by 4.6 million.

3. Let f(x)= x² - 6x and g(x)= 1- x

Find (fg)(5)

(fg)(5)= ____.

4. Find the inverse of the one-to-one function.

f(x)=6x+1

f^-1(x) =

(Use integers or fractions for any numbers in the expression.)

5. The regular price of a computer is x dollars. Let f(x) = x - 370 and g(x) = 0.7x.

a. Describe what the functions f and g model in terms of the price of the computer.

The function f gives the price of the computer___.

The function g gives the price of the computer____.

b. Find (fog)(x) and describe what this models in terms of the price of the computer.

(fog)(x) = __

The function (fog)(x) models the price of the computer after_____.

c. Find (gof)(x) and describe what this models in terms of the price of the computer.

(gof)(x) =

The function (g o f) f(x) models the price of the computer after____.

d. Which composite function models the greater discount on the computer. fog or gof? Why?

A. fog models the greater discount. since the 30% discount is taken on the regular price first.

B. gof models the greater discount, since the 70% discount is taken on the price after the 370% discount is applied to the regular price.

C. fog models the greater discount, since the 70% discount is taken on the regular price first.

D. gof models the greater discount, since the 30% discount is taken on the price after the $370 discount is applied to the regular price.

6. Use radical notation to rewrite the expression. Simplify. if possible.

256^3/4 + 8^2/3

Rewrite the expression using radical notation.
256^3/4 + 8^2/3 = _____ (Do not Simplify)

Now simplify.

256^3/4 + 8^2/3 = __

Solve the radical equation.

√(5x+9) +11= 4

7. Select the correct choice below and if necessary. fill in the answer box to complete your choice.

A. The solution set is { }.

(Type an exact answer. using radicals as needed. Use a comma to separate answers as needed.)

B. The solution is the empty set.