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Step Functions — Quiz Answers

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Which is the graph of g of x is equal to lceil x plus 3 rceil ?

A
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 5, negative 2) to (negative 4, negative 2). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (2, 5) to (3, 5).
B
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 3, negative 5) to (negative 2, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 2) to (5, 2).
C
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 5, negative 1) to (negative 4, negative 1). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (1, 5) to (2, 5).
D
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 2, negative 5) to (negative 1, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 1) to (5, 1).
2
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The cost of a single ticket depends on the number of tickets, t , purchased in a group, as represented by the function cap c times t c of t is equal to 18 point 5 0 dollars when 1 is less than or equal to t comma t is less than 12; c of t is equal to 16 point 0 0 dollars when 12 is less than or equal to t comma t is less than 20; c of t is equal to 14 point 5 0 dollars when 20 is less than or equal to t What is the total cost for 20 tickets?

A
14 point 5 0 dollars
B
290 point 0 0 dollars
C
16 point 0 0 dollars
D
320 point 0 0 dollars
3

An office supply store offers banner printing services. The store charges 4 dollars to print each one-foot-long section of a banner that is three feet tall. Which graph represents the cost to print a three-foot-tall banner that is x feet long?

A
Image with description On a coordinate plane, a graph titled Banner Printing Services shows Length of banner in feet on the x-axis and cost in dollars on the y-axis. A step graph has horizontal segments that are each 3 units long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The first segment goes from (0, 12) to (3, 12), the second segment goes from (3, 24) to (6, 24), the third segment goes from (6, 36) to (9, 36).
B
Image with description On a coordinate plane, a graph titled Banner Printing Services shows Length of banner in feet on the x-axis and cost in dollars on the y-axis. A step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (0, 4) to (1, 4). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (9, 40) to (10, 40).
C
Image with description On a coordinate plane, a graph titled Banner Printing Services shows Length of banner in feet on the x-axis and cost in dollars on the y-axis. A step graph has horizontal segments that are each 3 units long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The first segment goes from (0, 8) to (3, 8), the second segment goes from (3, 20) to (6, 20), the third segment goes from (6, 32) to (9, 32).
D
Image with description On a coordinate plane, a graph titled Banner Printing Services shows Length of banner in feet on the x-axis and cost in dollars on the y-axis. A step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (0, 8) to (1, 8). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (8, 40) to (9, 40).
4

What is the domain of the step function f of x is equal to lceil 2 x rceil minus 1 ?

A
start set x such that x is greater than or equal to negative 1 end set
B
start set x such that x is a real number end set
C
start set x such that x is greater than or equal to 1 end set
D
start set x such that x is an integer end set
5

A clothing store uses the step function f of x to recommend jeans sizes as a function of x , a child’s height in inches. f of x is equal to 1 when 40 is less than or equal to x comma x is less than 42; f of x is equal to 2 when 42 is less than or equal to x comma x is less than 44; f of x is equal to 3 when 44 is less than or equal to x comma x is less than 46; f of x is equal to 4 when 46 is less than or equal to x comma x is less than 48 According to the function, which is the height of a child who should wear size two jeans?

A
41 point 9 inches
B
44 point 1 inches
C
42 inches
D
44 inches
6

Which is the graph of the step function f of x ? f of x is equal to negative 1 when x is less than negative 1; f of x is equal to 0 when negative 1 is less than or equal to x comma x is less than or equal to 1; f of x is equal to 1 when x is greater than 1

A
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).
B
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).
C
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to the right at y = 1.
D
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has a closed circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has a closed circle at (1, 1) and continues horizontally to the right at y = 1.
7

Nina graphs the function y is equal to lfloor x rfloor to learn the properties of the parent floor function. What is the value of y when x is equal to 5 point 7 ?

A
6
B
5 point 7 5
C
5
D
5 point 5 0
8

Which is the graph of y is equal to lceil x rceil minus 2 ?

A
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 5, negative 5) to (negative 4, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 4) to (5, 4).
B
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 5, negative 5) to (negative 4, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 4) to (5, 4).
C
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 3, negative 5) to (negative 2, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 2) to (5, 2).
D
Image with description On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 4, negative 5) to (negative 3, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 3) to (5, 3).
9

If f of x is equal to negative 2 lceil x rceil plus 8 , what is f of negative 1 point 8 ?

A
4
B
6
C
12
D
10
10

A step function h of x is represented by y is equal to negative 2 lfloor x rfloor Which phrase best describes the range of the function h of x ?

A
all negative integers
B
all real numbers
C
all rational numbers
D
all even integers

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