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 only true for non-integer (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.

Question 2

Does your answer include the following?

Revolt · Accepted Answer

A: The statement is not true for all real numbers. It is only true for decimal or fractional values of x .; B: If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.; C: Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.

Question 3

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

Revolt · Accepted Answer

On the interval [0, 3), the graph of y  4⌊x  2⌋ consists of three horizontal steps. For 0 ≤ x < 1, the step is at y  8. For 1 ≤ x < 2, the step is at y  12. For 2 ≤ x < 3, the step is at y  16. Each step has a closed circle at the left endpoint and an open circle at the right endpoint.

Question 4

What is the domain of ?

Revolt · Accepted Answer

A: all real numbers

Question 5

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 0✔ multiples of 8 greater than 0.

Revolt · Accepted Answer

C: ✔ multiples of 8 greater than 0

Question 6

The domain of the function is all

Revolt · Accepted Answer

B: real numbers 0

Question 7

A parking garage allows users to park the first hour free and then charges $2.50 for each additional hour or fraction of an hour. Which equation represents this situation?

Revolt · Accepted Answer

C:

Question 8

Reread your description. Did it include the following?

Revolt · Accepted Answer

A: There are three steps.; B: The steps are at 8 from 0 to 1, at 12 from 1 to 2, and at 16 from 2 to 3.; C: Closed circles are on the left side of each step, and open circles are on the right.

Question 9

What is the range of ?

Revolt · Accepted Answer

C: all multiples of 4

Question 10

A gift card in the amount of $25 will purchase movies.

Revolt · Accepted Answer

3

Step Functions Answers

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