Step Functions

Question 1

Is the statement true for all real numbers? Explain.

Revolt · Accepted Answer

The statement is not true for all real numbers. It is true for noninteger decimal or fractional values of x, but not for integer values. For example, if x = 2, then ⌈2⌉ = 2 while ⌊3⌋ = 3.

Question 2

The domain of the function is all

Revolt · Accepted Answer

real numbers 0

Question 3

The range of the function is all

Revolt · Accepted Answer

integers 0

Question 4

Describe the graph of on [0, 3). Be specific in your description.

Revolt · Accepted Answer

There are three horizontal steps: y = 8 on [0, 1), y = 12 on [1, 2), and y = 16 on [2, 3). Each step has a closed circle on its left endpoint and an open circle on its right endpoint.

Question 5

What is the domain of ?

Revolt · Accepted Answer

all real numbers

Question 6

Gift cards are sold by an online store to purchase movies. A graph representing this situation is shown.This step function is discontinuous at all integers greater than 0multiples of 5 greater than 0multiples of 8 greater than 0.

Revolt · Accepted Answer

multiples of 8 greater than 0

Question 7

Evaluate:

Revolt · Accepted Answer

24

Question 8

Evaluate:

Revolt · Accepted Answer

24

Question 9

Which pair(s) of expressions are equal in value? Check all that apply.

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/EVresources/3111-11-04-20-02-task/mr001-1.jpg; Answer image: //media.edgenuity.com/EVresources/3111-11-04-20-02-task/mr001-3.jpg

Question 10

Is the statement true for all real numbers? Explain.

Revolt · Accepted Answer

The statement is not true for all real numbers. It is only true for noninteger (decimal or fractional) values of x. If x is an integer, the ceiling function ⌈x⌉ equals x, but the floor function ⌊x 1⌋ equals x 1. Since x does not equal x 1 for any integer, the equation does not hold when x is an integer.

Step Functions Answers

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