Step Functions — Quiz Answers

1

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What is the value of lfloor minus 12 rfloor ?

A

negative 12

B

12

C

13

D

negative 13

2

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Where is the graph of f of x is equal to 4 lfloor x minus 3 rfloor plus 2 discontinuous?

A

all integers

B

all real numbers

C

only at multiples of 3

D

only at multiples of 4

3

What is the value of lfloor 3 point 6 rfloor ?

A

3 point 6

B

3

C

4

D

3 point 5

4

What is the value of lfloor minus 1 point 1 rfloor ?

A

0

B

negative 2

C

1

D

negative 1

5

What is the value of lceil minus 4 point 6 rceil ?

A

negative 4

B

negative 4 point 5

C

negative 5

D

negative 4 point 6

6

Kareem wrote the expressions shown. lceil 3 point 2 rceil lfloor 2 point 7 rfloor lceil 2 point 9 rceil lfloor 4 point 8 rfloor Which pair is equivalent?

A

lfloor 4 point 8 rfloor and lceil 3 point 2 rceil

B

lceil 2 point 9 rceil and lfloor 2 point 7 rfloor

C

lfloor 2 point 7 rfloor and lceil 3 point 2 rceil

D

lceil 3 point 2 rceil and lceil 2 point 9 rceil

7

Which statement explains why the value of lfloor 2 point 4 rfloor is 2 but the value of lfloor minus 2 point 4 rfloor is negative 3 ?

A

because 2 point 4 rounds to 2 , and negative 2 point 4 rounds to negative 3

B

because 2 point 4 is positive, and negative 2 point 4 is negative

C

because 2 is the least integer greater than 2 point 4 , and negative 3 is the least integer greater than negative 2 point 4

D

because 2 is the greatest integer not greater than 2 point 4 , and negative 3 is the greatest integer not greater than negative 2 point 4

8

Which set of numbers best describes the possible values of x in the equation? lceil x minus 1 rceil is equal to lfloor x rfloor

A

all integer values of x

B

all real number values of x

C

only negative values of x

D

only noninteger values of x

9

Which statement describes the graph of f of x is equal to lfloor x rfloor minus 2 on left bracket 0 comma 3 right parenthesis ?

A

The steps are at y is equal to negative 2 for 0 is less than or equal to x comma x is less than 1 , at y is equal to negative 1 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to 0 for 2 is less than or equal to x comma x is less than 3 .

B

The steps are at y is equal to negative 3 for 0 is less than or equal to x comma x is less than 1 , at y is equal to negative 2 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to negative 1 for 2 is less than or equal to x comma x is less than 3 .

C

The steps are at y is equal to 1 for 0 is less than or equal to x comma x is less than 1 , at y is equal to 2 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to 3 for 2 is less than or equal to x comma x is less than 3 .

D

The steps are at y is equal to 0 for 0 is less than or equal to x comma x is less than 1 , at y is equal to 1 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to 2 for 2 is less than or equal to x comma x is less than 3 .

10

What is the value of 6 lceil 4 minus 9 point 4 rceil ?

A

negative 33

B

negative 32

C

negative 30

D

negative 36

11