PDF Graph each function. State the domain and range.

9-7 Special Functions

Graph each function. State the domain and range. 1. f (x) =

SOLUTION:

Make a table of values.

x

f (x)

0

0

0.5

0

1

0.5

1.5

0.5

2

1

2.5

1

3

1.5

Because the dots and circles overlap, the domain is all real numbers. The range is all integer multiples of 0.5.

2.

SOLUTION:

Make a table of values.

x

g(x)

0

0

0.5

0

1

?1

1.5

?1

2

?2

2.5

?2

3

?3

Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

3.

SOLUTION:

Make a table of values. eSolutions Manxual - Powered by Cohg(nxer)o

0

0

0.5

1

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9-7 Special Functions Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

3.

SOLUTION:

Make a table of values.

x

h(x)

0

0

0.5

1

1

2

1.5

3

2

4

2.5

5

3

6

Because the dots and circles overlap, the domain is all real numbers. The range is all integers. 4. SHIPPING Elan is ordering a gift for his dad online. The table shows the shipping rates. Graph the step function.

SOLUTION:

Graph the order total on the x-axis and the shipping cost on the y -axis. If the order total is greater than $0 but less than or equal to $15, the shipping cost will be $3.99. So, there is an open circle at (0, 3.99) and a closed circle at (15, 3.99). Connect these points with a line. Graph the rest of the data in the table similarly.

Graph each function. State the domain and range. 5. f (x) = |x - 3|

eSolutSioOnsLMUanTuIaOl -NPo: wered by Cognero Since f (x) cannot be negative, the minimum point of the graph is where f (x) = 0.

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9-7 Special Functions

Graph each function. State the domain and range. 5. f (x) = |x - 3|

SOLUTION: Since f (x) cannot be negative, the minimum point of the graph is where f (x) = 0.

Make a table of values. Be sure to include the domain values for which the function changes.

x

0

1

2

3

4

f (x)

3

2

1

0

1

The graph will cover all possible values of x, so the domain is all real numbers.The graph will go no higher thany = 0, so range is {y | y 0}.

6. g(x) = |2x + 4| SOLUTION: Since g(x) cannot be negative, the minimum point of the graph is where g(x) = 0.

Make a table of values.Be sure to include the domain values for which the function changes.

x

?3

?2

?1

0

1

g(x)

2

0

2

4

6

The graph will cover all possible values of x, so the domain is all real numbers.The graph will go no higher than y = 0, so and the range is {y | y 0}.

7.

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SOLUTION: This is a piecewise-defined function. Make a table of values. Be sure to include the domain values for which the

9-7 STpheecgiarlapFhuwnciltliocnovser all possible values of x, so the domain is all real numbers.The graph will go no higher than y = 0, so and the range is {y | y 0}.

7.

SOLUTION:

This is a piecewise-defined function. Make a table of values. Be sure to include the domain values for which the function changes.

x

?3

?2

?1

0

1

f (x)

3

2

1

?1

1

Notice that both functions are linear.

The graph will cover all possible values of x, so the domain is all real numbers. The graph will go no lower than y = -3, so the range is {y | y > -3}.

8.

SOLUTION:

This is a piecewise-defined function. Make a table of values. Be sure to include the domain values for which the function changes.

x

?4

?3

?2

?1

0

g(x) 5

4

3

1

?2

Notice that both functions are linear.

The graph will cover all possible values of x, so the domain is all real numbers. The graph will cover all possible values of y , so the range is all real numbers.

Graph each function. State the domain and range. 9.

SOLUTION:

Make a table of values. eSolutions Mxanual - Pofw(exre)d by Cognero

0

0

0.5

0

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9-7 STpheecgiaral pFhuwnciltlicoonvser all possible values of x, so the domain is all real numbers. The graph will cover all possible values of y , so the range is all real numbers.

Graph each function. State the domain and range. 9.

SOLUTION:

Make a table of values.

x

f (x)

0

0

0.5

0

1

3

1.5

3

2

6

2.5

6

3

9

Because the dots and circles overlap, the domain is all real numbers. The range is all integer multiples of 3.

10.

SOLUTION:

Make a table of values.

x f (x)

0

0

0.5 ?1

1

?1

1.5 ?2

2

?2

2.5 ?3

3

?3

Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

11. g(x) =

SOLUTION: Make a table of values.

x eSolutions Manual - Pow0ered by Cognero

0.5 1

g (x) 0 0 ?2

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9-7 Special Functions Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

11. g(x) =

SOLUTION:

Make a table of values.

x

g (x)

0

0

0.5

0

1

?2

1.5

?2

2

?4

2.5

?4

3

?6

Because the dots and circles overlap, the domain is all real numbers. The range is all even integers.

12. g(x) =

SOLUTION:

Make a table of values.

x

g (x)

0

3

0.5

3

1

4

1.5

4

2

5

2.5

5

3

6

Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

13. h(x) =

SOLUTION:

Make a table of values.

x

h(x)

0

?1

eSolutions Manu0a.l5- Powered by Cogner?o1

1

0

1.5

0

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9-7 Special Functions Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

13. h(x) =

SOLUTION:

Make a table of values.

x

h(x)

0

?1

0.5

?1

1

0

1.5

0

2

1

2.5

1

3

2

Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

14. h(x) =

+ 1

SOLUTION:

Make a table of values.

x

h(x)

0

1

0.5

1

1

1.5

1.5

1.5

2

2

2.5

2

3

2.5

Because the dots and circles overlap, the domain is all real numbers. The range is all integer multiples of 0.5.

15. CAB FARES Lauren wants to take a taxi from a hotel to a friend's house. The rate is $3 plus $1.50 per mile after the first mile. Every fraction of a mile is rounded up to the next mile. a. Draw a graph to represent the cost of using a taxi cab. b. What is the cost if the trip is 8.5 miles long?

SOLUTION: eSolutaio.nMs Maakneuaal -taPbolweeorefdvbaylCuoegsn.ero

Number of Miles

Cost

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9-7 Special Functions Because the dots and circles overlap, the domain is all real numbers. The range is all integer multiples of 0.5.

15. CAB FARES Lauren wants to take a taxi from a hotel to a friend's house. The rate is $3 plus $1.50 per mile after the first mile. Every fraction of a mile is rounded up to the next mile. a. Draw a graph to represent the cost of using a taxi cab. b. What is the cost if the trip is 8.5 miles long?

SOLUTION: a. Make a table of values.

Number of Miles

Cost

0

3 + 1.5(0) = 3

0.5

3 + 1.5(0) = 3

1

3 + 1.5(0) = 3

1.5

3 + 1.5(1) = 4.5

2

3 + 1.5(1) = 4.5

2.5

3 + 1.5(2) = 6

3

3 + 1.5(2) = 6

b. To find the cost if the trip is 8.5 miles long, round 8.5 to 9. Subtract the first mile that does not incur additional milage cost, 9-1 = 8.Then, multiply 8 by 1.5 and add 3 to the result. So, the cost of an 8.5-mile trip is 3 + 1.5(8) or $15.

16. CCSS MODELING The United States Postal Service increases the rate of postage periodically. The table shows the cost to mail a letter weighing 1 ounce or less from 1995 through 2009. Draw a step graph to represent the data.

SOLUTION: Graph the year on the x-axis and the postage on the y -axis. If the year is greater than or equal to1995 but less than 1999, the postage will be $0.32. So, there is an closed circle at (1995, 0.32) and a open circle at (1999, 0.32). Connect these points with a line. Graph the rest of the data in the table similarly.

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