1.

Evaluate each expression based on the following table.

x	3	2	1	0	1	2	3
f(x)	1	3	6	1	3	1.5	0.25

(a)

f(1)f(1)

(b)

f(1)f(2)

(c)

3f(2)

2.

Crude Oil Production: Mexico The following table shows daily crude oil production by a country's national oil company, for2008-2014

(t= 0

represents 2008).

Yeart (Year since 2008)	0	1	2	3	4	5	6
Crude Oil Production p(t) (million barrels/day)	3.14	2.98	2.97	2.96	2.91	2.85	2.73

(a)

Find

p(1),p(2), andp(6).

p(1) =

Interpret your answer.

In the year ,the country's national oil company produced millionbarrels of crude oil per day.

p(2) =

Interpret your answer.

In the year ,the country's national oil company produced millionbarrels of crude oil per day.

p(6) =

Interpret your answer.

In the year ,the country's national oil company produced millionbarrels of crude oil per day.

(b)

Findp(5)p(1).

p(5)p(1) =

Interpret your answer.

Crude oil production by the country's national oil company decreased by millionbarrels of crude oil per day between the years and .

3.

Refer to the following graph which shows the numberf(t) of housing starts for single-family homes in a country each year from 2000 through 2014

(t= 0

represents 2000, andf(t) is the number of housing starts in yeartin thousands of units).

A graph has a horizontalt-axis with values from 0 to 14 and a verticalf(t)-axis with values from 0 to 2200. The graph contains a series of 15 points connected by line segments. The segments and the approximate points they connect are as follows.

• The segments start at(0, 1400),
• go up and right to(1, 1500),
• go up and right to(2, 1600),
• go up and right to(3, 1700),
• go up and right to(4, 1800),
• go up and right to(5, 1900),
• go down and right to(6, 1700),
• go down and right to(7, 1200),
• go down and right to(8, 800),
• go down and right to(9, 600),
• go up and right to(10, 700),
• go down and right to(11, 600),
• go up and right to(12, 700),
• go up and right to(13, 800),
• and go right to stop at(14, 800).

Estimatef(9).

f(9) =

Interpret your answer.

There were 600,000 housing starts in 2009.There were 700,000 housing starts in 2009. There were 750,000 housing starts in 2012.There were 800,000 housing starts in 2009.There were 1.7 million housing starts in 2006.

Estimatef(13).

f(13) =

Interpret your answer.

There were 600,000 housing starts in 2013.There were 700,000 housing starts in 2013. There were 750,000 housing starts in 2012.There were 800,000 housing starts in 2013.There were 1.7 million housing starts in 2006.

Estimatef(12.5).

f(12.5) =

Interpret your answer.

There were 600,000 housing starts in the year beginning July 2012.There were 700,000 housing starts in the year beginning July 2012. There were 750,000 housing starts in the year beginning July 2012.There were 800,000 housing starts in the year beginning July 2013.There were 1.7 million housing starts in the year beginning July 2006.

4.

Givenf(x) =x²+3x+8, find the following.

(a)

f(0)

(b)

f(1)

(c)

f(1)

(d)

f(3)

(e)

f(a)

(f)

f(x+h)

5.

Givenf(x) =5x7, find the following.

(a)

f(1)

(b)

f(0)

(c)

f(1)

(d)

f(y)

(e)

f(a+b)

6.

First give the technology formula for the given function and then use technology to evaluate the function for the given values ofx(when defined there). (Round all answers to four decimal places.)

h(x) =

x²1

x²+1

;x= 0.5, 1.5, 2.5,, 10.5

(x^2 + 1)/(x^21)(x^21)/(x^2 + 1) (x1)^2/(x+ 1)^2(x1)^2/(x^2 + 1)

h(0.5)=h(1.5)=h(2.5)=h(3.5)=h(4.5)=h(5.5)=h(6.5)=h(7.5)=h(8.5)=h(9.5)=h(10.5)=

7.

In the following graph,n(t) is a certain store's approximate net income, in millions of dollars, for the year ending at timet(tis time in years since December 2004).

On the coordinate plane the horizontal axis is labeledtand the vertical axis is labeled n(t). The curve enters the window at approximately 249 units above the origin, goes up and right becoming less steep, passes through approximately 2 units right of and approximately 603 units above the origin, changes direction at approximately 2.79 units right of and approximately 627 units above the origin, goes down and right becoming more steep, passes through approximately 4 units right of and approximately 589 units above the origin, passes through approximately 4.5 units right of and approximately 559 units above the origin, passes through approximately 4.75 units right of and approximately 543 units above the origin, goes down and right becoming less steep, changes direction at approximately 6.7 units right of and approximately 460 units above the origin, goes up and right becoming more steep, and exits the window at approximately 9 units right of and approximately 700 units above the origin.

(a)

Estimaten(2),n(4), andn(4.5) to the nearest 50.

n(2) =

Interpret your answer.

In the year , the store's net income was $ million.

n(4) =

Interpret your answer.

In the year , the store's net income was $ million.

n(4.5) =

Interpret your answer.

In the year ending ---Select--- June 2004 June 2006 June 2009 , the store's net income was$ million.

(b)

At approximately which value oftin the interval [3, 8] isn(t)increasingmost rapidly?

t=

Interpret your answer.

Between December 2007 and December 2012, the store's net income was increasing most rapidly in ---Select--- December 2007 December 2009 December 2012 .

(c)

At approximately which value oftin the interval [3, 8] isn(t)decreasingmost rapidly?

t=

Interpret your answer.

Between December 2007 and December 2012, the store's net income was decreasing most rapidly in ---Select--- December 2007 December 2009 December 2012 .

8.

Sketch the graph of the given function.

f(x) =

x		if3x<0
5		if 0x3

Evaluate the given expressions.

f(1)	=
f(0)	=
f(1)	=

Use technology to duplicate the graphs. Give the technology formula. HINT [See Example 2.](x)*(x<= 0) + (5)*(x>0)(x)*(x<0) + (5)*(x>= 0) (x)*(x<0) + (5)*(x<= 3)(x)*(x>=

3)

+ (5)*(x>= 0)

9.

Say whether or notf(x) is defined for the given values ofx. If it is defined, give its value. (If an answer is undefined, enter UNDEFINED.)

f(x) =x

1

x²

, with domain (0, +)

(a)

x=7

f(7) =

(b)

x= 0

f(0) =

(c)

x=5

f(5) =

10.

The value of the Conference Board Index of 10 economic indicators in the United States could be approximated by the following function of timetin months since the end of December 2002.

E(t) =

0.4t+100	if 6t15
0.2t+109	if 15<t20.

(a)

Estimate

E(7),E(17), andE(20).

E(7)	=
E(17)	=
E(20)	=

Interpret your answers.

E(7)

means in ---Select--- January February March April May June July August September October November December of the year the Conference Board Index was .

E(17)

means in ---Select--- January February March April May June July August September October November December of the year the Conference Board Index was .

E(20)

means in ---Select--- January February March April May June July August September October November December of the year the Conference Board Index was .

(b)

Sketch the graph ofE. Use your graph to estimate when the index first reached103.

t=

(c)

Use technology to generate a table of values forE(t) with

t= 6, 7,, 20.

t	6	7	8	9	10
E(t)

t	11	12	13	14	15
E(t)

t	16	17	18	19	20
E(t)