Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The Floor and $C E I L I N G$ functions are defined as follows:$$\begin{array}{l}y=f \ln (x)=\left\{\begin{array}{c}x, \text { if } x \text { is an integer } \\\text { integer to } x \text { 's left, otherwise }\end{array}\right. \\y=\operatorname{ceil}(x)=\left\{\begin{array}{c}x \text { if } x, \text { is an integer } \\\text { integer to } x \text { 's right otherwise }\end{array}\right.\end{array}$$ Use these functions to solve.(a) $\operatorname{ceil}(5),$ (b) $\operatorname{ceil}(-5),$ (c) $\operatorname{ceil}(5.1),$ (d) $\operatorname{ceil}(-5.1)$

(a) 5(b) -5(c) 6(d) -5

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Campbell University

McMaster University

Harvey Mudd College

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

03:18

03:31

The Floor and $C E I L I N…

02:08

02:39

03:40

02:05

03:21

5.3.28Let f(x) = In x …

01:34

The function $f(x)=[x]^{2}…

Let $\mathrm{f}(\mathrm{x}…

01:39

Let $f(x)=\left\{\begin{ar…

we've got two new functions were looking at the floor function and the ceiling function. So let's take a look at what these two functions, uh, do what they have in common and how they're different. In both cases, if you put in an integer, you get out, just the energy you put in. Nothing changes. So if you put in an integer like 10, you're going to get out. 10 In either case, floor or ceiling floor says that if it's not an integer, we're going to take the integer, the next integer to the left. Okay, so in other words, if I have a number line, let's say I have 12 and three if I have a number right here, it 2.5 the floor function says, I'm gonna move down to the left, so that would give me too. Another way to think of that is, let's make this number line stand on its head, okay? And they go up like a like a like a hotel or something. First floor, second floor, third floor. If I have a number 2.5, the floor function says, I'm going to sink to the floor. Okay, so the next floor that that would go to would be to that's the equivalent of going left on the number line ceilings. The opposite ceiling says If it's not an integer, I'm going to go to the next integer to the right. So in the case of my 2.5, I'm going to go up to three on this vertical number line. That would be like saying, OK, I'm in between floors. I'm sealing says. I'm gonna go up to the ceiling again. That would give me three. So going up on that vertical number line is equivalent to going right on the horizontal line. So let's use our ceiling function to find a few values. Okay, first, let's do some integers. Well, what's the ceiling of five? If it's an image, er, you just get out what you put in. So what equals five? Does it matter if it's a positive image or or a negative image? Er, so if I have the ceiling of negative five still in imager, still no change. Now let's take something that's not an immature ceiling of 5.1. Well, that means I'm going to take the next imager to the right, which means I'm going to go up and it's gonna go up to six again. If I had that the 5456 on this number line and I was just a little bit above five, it would rise up to the ceiling would rise up to six. It's important that we take a negative number, though, because negatives sometimes your little counterintuitive for a ceiling. We think we're going up, so it's very tempting to go o negative 5.1. We're gonna go up to negative six. It mirrors the positives, but it doesn't think about what that looks like. If I have the number line and I'll have negative three negative four negative five negative six that's negative. 5.1 is actually a little bit below negative five. So if I'm going to the next image or to the right, I'm actually going up to negative five. So it's important Thio for the negatives to make sure you're going the right direction. Most the time. The positives make intuitive sense. You're going up to the next image or you're going up to six. Make sure you're going the right direction with your negatives, so these are four different outcomes from using our new ceiling function

View More Answers From This Book

Find Another Textbook

Numerade Educator

sketch the graph of the given ellipse, labeling all intercepts.$$\begin{…

01:05

You are given a pair of equations, one representing a supply curve and the o…

03:41

Sometimes when one plots a set of data, it appears to be piece wise linear, …

02:22

a) sketch the graph of the given function, and then draw the tangent line at…

02:13

Find the slope of the line passing through each pair of points.$$(12,16) \te…

01:32

Compute the indicated limit.$$\text { (a) } \lim _{x \rightarrow 5^{+}} …

01:50

Refer to Figures $8,9,$ and $10 .$ In each case, choose another point on the…

01:29

Solve each of the following equations for the real values of $x$.$$x^{4}…

02:36

Find the indicated limit.$$\lim _{x \rightarrow 3} \frac{x^{2}-7 x+12}{x…

01:45

Use the zeros, vertical and horizontal asymptotes along with the sign of the…