For the functions f(x) and g(x), evaluate the indicated function.
-The amount of money, in billions of dollars, spent on health care that was covered by insurance in a certain country in a particular year can be approximated by the function f(x) = x2 + 14x + 279,
Where x represents the number of years after 2005. The amount of money, in billions of dollars,
Spent on health care that was paid out of pocket in a certain country in a particular year can be
Approximated by the function g(x) = 9x + 149, where again x represents the number of years after
2005. (i) Find

( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } )

. Explain, in your own words, what this function represents.
(ii) Find (

\mathrm { f } - \mathrm { g } ) ( 60 )

. Explain, in your own words, what this number represents.
A) (i)

( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428

; this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars,

x

years after

2005 .

(ii) 1792 ; health-care costs covered by insurance will be

\$ 1,792,000,000,000

less than health-care costs that are paid out of pocket in

2065 .

B) (i)

( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130

; this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars,

x

years after

2005 .

(ii) 4030 ; health-care costs covered by insurance will be

\$ 4,030,000,000,000

higher than health-care costs that are paid out of pocket in

2065 .

C) (i)

( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130

; this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars,

x

years after 2005 .
(ii) 4030 ; health-care costs covered by insurance will be

\$ 4,030,000,000,000

less than health-care costs that are paid out of pocket in

2065 .

D) (i)

( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428

; this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars,

x

years after

2005 .

(ii) 1792 ; health-care costs covered by insurance will be

\$ 1,792,000,000,000

higher than health-care costs that are paid out of pocket in

2065 .

Without Graphing the Function, State the Shift(s) That Are Applied f(x)=(x+50)2−90f ( x ) = ( x + 50 ) ^ { 2 } - 90f(x)=(x+50)2−90

Multiple Choice

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Without Graphing the Function, State the Shift(s) That Are Applied $f ( x ) = ( x + 50 ) ^ { 2 } - 90$

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