Graph each function. Identify the domain and

[Pages:19]2-6 Special Functions Graph each function. Identify the domain and range.

1.

SOLUTION:

The y-coordinates of points on the graph are real numbers less than or equal to 4, so the range

is

.

2. SOLUTION:

The function is defined for all real values of x, so the domain is all real numbers.

D = {all real numbers}

The y-coordinates of points on the graph are real numbers less than or equal to 4, so the range

is

.

The function is defined for all real values of x, so the domain is all real numbers.

D = {all real numbers}

The y-coordinates of points on the graph are real numbers between 8 and ?2 and less than or equal to

?8, so the range is

.

Write the piecewise-defined function shown in each graph.

2.

SOLUTION:

The function is defined for all real values of x, so the domain is all real numbers.

D = {all real numbers}

The y-coordinates of points on the graph are real eSolutniounms Mbaenrsuabl e- tPwoweeerned8baynCdog?n2eraond less than or equal to

?8, so the range is

.

3.

SOLUTION:

The left portion of the graph is the line g(x) = x + 4. There is an open circle at (?2, 2), so the domain for

this part of the function is

.

The center portion of the graph is the constant function g(x) = ?3. There are closed dots at (?2, ?3) and (3, 3), so the domain for this part is

. The right portion of the graph is the line g(x) = ?2x + 12. There is an open circle at (3, 6), so the domain

for this part is

.

Page 1

Write the piecewise function.

D = {all real numbers}

The y-coordinates of points on the graph are real

2-6 SnpuemcbiaelrsFbuentwcteioenns8 and ?2 and less than or equal to

?8, so the range is

.

Write the piecewise-defined function shown in each graph.

3.

SOLUTION:

The left portion of the graph is the line g(x) = x + 4. There is an open circle at (?2, 2), so the domain for

this part of the function is

.

The center portion of the graph is the constant function g(x) = ?3. There are closed dots at (?2, ?3) and (3, 3), so the domain for this part is

. The right portion of the graph is the line g(x) = ?2x + 12. There is an open circle at (3, 6), so the domain

for this part is

.

Write the piecewise function.

4.

SOLUTION:

The left portion of the graph is the constant function g(x) = 6. There is a closed dot at (?5, 6), so the

domain for this part is

.

The center portion of the graph is the line g(x) = ?x + 4. There are open circles at (?5, 9) and (?2, 6), so

the domain for this part is

.

The right portion of the graph is the line

. There is a closed dot at (?2, 0), so

the domain for this part is

.

Write the piecewise function.

4.

SOLUTION:

The left portion of the graph is the constant function g(x) = 6. There is a closed dot at (?5, 6), so the

domain for this part is

.

eSolutTiohnes Mceanutearl -pPoorwtieorendobfy tChoegngerraoph is the line g(x) = ?x + 4. There are open circles at (?5, 9) and (?2, 6), so

the domain for this part is

.

5. CCSS REASONING Springfield High School's theater can hold 250 students. The drama club is performing a play in the theater. Draw a graph of a step function that shows the relationship between the number of tickets sold x and the minimum number of performances y that the drama club must do.

SOLUTION: When x is greater than 0 and less than or equal to 250, the drama club needs to do only one performance. When x is greater than 250 and less than or equal to 500, they must do at least two performances. Continue the pattern with a table.

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2-6 Special Functions

5. CCSS REASONING Springfield High School's theater can hold 250 students. The drama club is performing a play in the theater. Draw a graph of a step function that shows the relationship between the number of tickets sold x and the minimum number of performances y that the drama club must do.

SOLUTION: When x is greater than 0 and less than or equal to 250, the drama club needs to do only one performance. When x is greater than 250 and less than or equal to 500, they must do at least two performances. Continue the pattern with a table.

Graph each function. Identify the domain and range. 6.

SOLUTION:

D = {all real numbers} The function g(x) is a reflection of twice of a greatest integer function. So, g(x) takes all even integer values or zero. R = {all even integers}

7.

SOLUTION:

Graph each function. Identify the domain and range. 6. SOLUTION:

D = {all real numbers}

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The function g(x) is a reflection of twice of a greatest integer function. So, g(x) takes all even

D = {all real numbers} R = {all integers}

Graph each function. Identify the domain and range.

8.

SOLUTION:

Page 3

D = {all real numbers} 2-6 SRp=ec{iallFinutnegcetiros}ns

Graph each function. Identify the domain and range. 8.

SOLUTION:

D = {all real numbers} .

10.

SOLUTION:

D = {all real numbers}

9. SOLUTION:

D = {all real numbers} .

11. SOLUTION:

D = {all real numbers} .

10. SOLUTION:

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D = {all real numbers} .

Graph each function. Identify the domain and range.

12.

SOLUTION:

Page 4

D = {all real numbers} 2-6 Special Functions .

. .

Graph each function. Identify the domain and

range.

14.

12. SOLUTION:

SOLUTION:

. .

13. SOLUTION:

. .

14.

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SOLUTION:

D = {all real numbers} .

15. SOLUTION:

.

Write the piecewise-defined function shown in each graph.

16.

SOLUTION:

Page 5

The left portion of the graph is the constant function g(x) = ?8. There is a closed dot at (?6, ?8), so the

2-6 Special Functions .

Write the piecewise-defined function shown in each graph.

16.

SOLUTION:

The left portion of the graph is the constant function g(x) = ?8. There is a closed dot at (?6, ?8), so the

domain for this part of the function is

.

The center portion of the graph is the line g(x) = 0.25x + 2. There are closed dots at (?4, 1) and (4, 3),

so the domain for this part is

.

The right portion of the graph is the constant function g(x) = 4. There is an open circle at (6, 4), so the

constant function is defined for

.

Write the piecewise function.

17.

SOLUTION:

The left portion of the graph is the line g(x) = ?x ? 4. There is an open circle at (?3, ?1), so the domain for

this part of the function is

. The center portion of the graph is the line g(x) = x + 1. There are closed dots at (?3, ?2) and (1, 2), so the

domain for this part is

.

The right portion of the graph is the constant function g(x) = ?6. There is an open circle at (4, ?6), so the

domain for this part is

.

Write the piecewise function.

17.

SOLUTION:

The left portion of the graph is the line g(x) = ?x ? 4. There is an open circle at (?3, ?1), so the domain for

this part of the function is

. The center portion of the graph is the line g(x) = x + eSolut1io.nTs hMearneuaalr-ePcowloesreeddbdyoCtosganter(o?3, ?2) and (1, 2), so the

domain for this part is

.

18.

SOLUTION:

The left portion of the graph is the constant function g(x) = ?9. There is an open circle at (?5, ?9), so the

domain for this part of the function is

.

The center portion of the graph is the line g(x) = x + 4. There are closed dots at (0, 4) and (3, 7), so the

domain for this part is

.

The right portion of the graph is the line g(x) = x ? 3.

There is an open circle at (7, 4), so the domain foPrage 6

this part is

.

2-6 Special Functions

18.

SOLUTION:

The left portion of the graph is the constant function g(x) = ?9. There is an open circle at (?5, ?9), so the

domain for this part of the function is

.

The center portion of the graph is the line g(x) = x + 4. There are closed dots at (0, 4) and (3, 7), so the

domain for this part is

.

The right portion of the graph is the line g(x) = x ? 3. There is an open circle at (7, 4), so the domain for

this part is

.

Write the piecewise function.

19.

SOLUTION:

The left portion of the graph is the constant function g(x) = 8. There is a closed dot at (?1, 8), so the

domain for this part is

.

The center portion of the graph is the line g(x) = 2x. There are closed dots at (4, 8) and (6, 12), so the

domain for this part is

.

The right portion of the graph is the line g(x) = 2x ? 15. There is a circle at (7, ?1), so the domain for this

part is

.

Write the piecewise function.

19.

SOLUTION:

The left portion of the graph is the constant function g(x) = 8. There is a closed dot at (?1, 8), so the

domain for this part is

.

The center portion of the graph is the line g(x) = 2x. There are closed dots at (4, 8) and (6, 12), so the

domain for this part is

.

eSolutTiohnes Mriagnhutapl -oPrtoiwoenreodfbtyhCeoggrnaeproh is the line g(x) = 2x ? 15. There is a circle at (7, ?1), so the domain for this

part is

.

Graph each function. Identify the domain and range. 20.

SOLUTION:

D = {all real numbers} R = {all integers}

21.

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2-6 Special Functions

Graph each function. Identify the domain and range. 20.

SOLUTION:

D = {all real numbers} R = {all integers} 22. SOLUTION:

D = {all real numbers} R = {all integers} 21. SOLUTION:

D = {all real numbers} R = {all integers} 22. SOLUTION:

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D = {all real numbers}

D = {all real numbers} R = {all integers} 23. SOLUTION:

The function is defined for all real values of x, so the domain is all real numbers. D = {all real numbers} The function g(x) is twice of a greatest integer function. So, g(x) takes only even integer values. Therefore, the range is R = {all even integers}. Graph each function. Identify the domain and range. 24. SOLUTION:

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