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Inspiration from this brand.
Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them.
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Customers like the appearance, value, and smell of the aroma diffuser. They mention that it looks great, smells wonderful, and is great value for the price. That said, some complain about the fit and performance. They say that the plug ins do not fit and that the product did not work.
AI-generated from the text of customer reviews
Customers are satisfied with the appearance of the aroma diffuser. They mention that it looks great, and the design is simple.
"I love that it's a nightlight and that the design is simply and matches everything." Read more
"These look great and work very well with his sents" Read more
"The plugins from Homeworx look fabulous and provide nice level of light at night but finding a refill for the potpouuri is impossible!..." Read more
Customers are satisfied with the smell of the aroma diffuser. They mention that it smells wonderful.
"Great purchase, easy to install, smells great " Read more
" Great scents by Harry . Beautiful vessels" Read more
" Good fragrance ..." Read more
Customers are satisfied with the value of the aroma diffuser. They mention that it is a great purchase and a good value for the price.
" Great purchase , easy to install, smells great" Read more
" Great value for the price !!!" Read more
"Cute, affordable , great quality!..." Read more
Customers are dissatisfied with the fit of the aroma diffuser. They mention that it does not fit the Harry Slatkin Homeworx refillable bottles and plug-ins.
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Customers are dissatisfied with the performance of the aroma diffuser. They mention that it does not work as expected.
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Homework is work that teachers give students to complete outside of the school day. Homework is meant to provide students with practice for what was learned in school or an extension of what was done in class. Students are expected to complete the homework and return to school with the completed homework assignment.
Most teachers give students homework so that they can practice something that was taught to them during class.
For example, if a teacher is teaching students how to add decimal numbers then the homework assignment would be for students to try adding decimals at home independently.
In my science class I never give my students homework that isn’t meaningful or practice towards a learning standard.
Gone are the days of giving homework that is “busy work”.
Also, when students return the following day their homework assignment is incorporated into the lesson so they quickly figure out that completing homework is necessary.
Some teachers, myself included, will use homework as a formative assessment.
If you are unsure what formative assessments are then you need to check out this article I wrote recently.
Homework can be almost anything.
Some examples of homework may include a simple worksheet to complete, a long term project, research, reading, a journal entry, completing something online, a drawing, or the continuation of something started in school, and just about anything else.
Homework isn’t limited to one specific thing.
With my eight grade students I have assigned videos for them to watch, creating a slideshow, completing a CER (more about the CER here) , conduct a survey for data collection, and more.
I have even had them collect leaves to identify the following day in our science class!
If you are a teacher reading this make sure to make your homework assignments interesting and worthwhile, don’t just assign homework as busy work.
No, teachers don’t have to give homework.
Usually teachers have discretion whether or not they are going to assign homework.
Personally, the principal or school district I work for has no idea how often I assign homework or what I assign for homework.
This decision to give or not give homework solely comes down to the classroom teacher.
The importance of homework is a heavily debated topic these days.
On one hand you have teachers that will say it is necessary that students continue learning outside the classroom in order to be more successful inside the classroom.
On the other hand some teachers will say that homework isn’t necessary as long as students are working hard during the school day.
Another reason homework is seen as not necessary is because students these days are so busy out of school that they don’t have time to complete homework.
Who is right?
I’d say it’s probably somewhere in the middle.
There is nothing wrong with a little homework for students but it shouldn’t be assigned every night.
I (Allen) am currently teaching at a public school in a western suburb of Chicago. My teaching career started in 2004. Some of my interests outside of teaching is being with my family, biking, playing video games, travelling, and making the Teacher Adviser website.
What Are Formative Assessments?
Formative assessments are assessments (feedback) used by the teacher to determine student learning during a unit. The teacher uses formative assessments to determine how they are going to teach or...
What Are Summative Assessments?
Summative assessments are the assessments/tests that are used to determine student understanding of a specific learning standard after the learning or practice has taken place. Summative assessments...
Sets of Points Functions at Points Functions into Functions Domains & Decompositions Word Probs Inverse Functions
Thus far, we have done composition by points, with those points either listed in sets or else displayed on graphs; and we have evaluated compositions at given input values.
We can also evaluate compositions symbolically; that is, without a numerical input value.
Content Continues Below
Composite Functions
In practice, there is not much difference between evaluating a function at a formula or expression, and composing two functions. There's a notational difference, of course, but evaluating f ( x ) at y 2 , on the one hand, and composing f ( x ) with g ( x ) = y 2 , on the other hand, have you doing the exact same steps and getting the exact same answer. So you've actually kinda already done function composition.
Until now, when you were given a function f ( x ) , you could plug a number or another variable in for x . You could even get fancy and plug in an entire expression for x . For example, given f ( x ) = 2 x + 3 , you could find f ( y 2 − 1) by plugging y 2 − 1 in for x to get:
f ( y 2 − 1) = 2( y 2 − 1) + 3 = 2 y 2 − 2 + 3 = 2 y 2 + 1
In function composition, you're usually plugging entire functions in for the x . In other words, when you're doing composition of functions, you're almost always "getting fancy" with what you're plugging in to a function.
It is simpler to evaluate a composition at a point because you can simplify as you go, since you'll always just be plugging in numbers and simplifying at each step.
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On the other hand, evaluating a symbolic compositon, where you're first plugging x into some function and then plugging that function into some other function, can be much messier. But the process works just as the at-a-number composition does, and using parentheses — to be carefully explicit at each step — will be even more helpful.
In this composition, I am not trying to find a certain numerical value. Instead, I am trying to find the formula that results from plugging the formula for g ( x ) into the formula for f ( x ) .
I will write the formulas at each step, using parentheses to indicate where the inputs should go:
( f ∘ g )( x ) = f ( g ( x ))
= f (− x 2 + 5)
= 2( ) + 3
= 2(− x 2 + 5) + 3
= −2 x 2 + 10 + 3
= −2 x 2 + 13
This final line, being as simplified as I can go, gives me my answer.
( f ∘ g )( x ) = −2 x 2 + 13
If you plug in 1 for the x in the above, you will get:
( f ∘ g )(1) = −2(1) 2 + 13
= −2 + 13 = 11
This is the same answer we got before , when we were evaluating at a point. Previously, we'd plugged a number into g ( x ) , found a new value, plugged that value into f ( x ) , and simplified the result. This time, we plugged a formula into f ( x ) , simplified the formula, plugged the same number in as before, and simplified the result. The final numerical answers were the same.
If you've done the symbolic composition (the composition with the formulas) correctly, you'll get the same values either way, regardless of the value you pick for x . This can be a handy way of checking your work.
In this exercise, I'll be doing the plug-n-chug in the opposite order from the previous exercise.
( g ∘ f )( x ) = g ( f ( x ))
= g (2 x + 3)
= −( ) 2 + 5
= −(2 x + 3) 2 + 5
= −(4 x 2 + 12 x + 9) + 5
= −4 x 2 − 12 x − 9 + 5
= −4 x 2 − 12 x − 4
This doesn't simplify any further, so I'm done.
( g ∘ f )( x ) = −4 x 2 − 12 x − 4
There is something you should note from these two symbolic examples. Look at the results I got:
( g ∘ f )( x ) = −4 x 2 − 12 x − 4
That is, ( f ∘ g )( x ) is not the same as ( g ∘ f )( x ) . This is true in general. You should assume that the compositions ( f ∘ g )( x ) and ( g ∘ f )( x ) are going to be different.
In particular, composition is not the same thing as multiplication. The open dot " ∘ " is not the same as a multiplication dot " • ", nor does it mean the same thing.
Multiplication: always true
f ( x ) • g ( x ) = g ( x ) • f ( x )
Composition: usually false
( f ∘ g )( x ) = ( g ∘ f )( x )
You cannot reverse the order in composition and expect to end up with the same result. Composition is not flexible like multiplication; composition is an entirely different process. Do not try to multiply functions when you are supposed to be plugging them into each other.
By the way, if you remember learning about the associative, commutative, and transitive properties of real numbers, and if you remember wondering, "Why do I need to know this stuff?", this is why: so that you can recognize here that the commutative property does not hold. Function composition is an operation which is not commutative.
Do not mistake this composition as being the square of the function f ( x ) . Because function composition is not commutative, the result will *not* be equal to ( f ( x )) 2 , which is 4 x 2 + 12 x + 9 . Instead, I get:
( f ∘ f )( x ) = f ( f ( x ))
= f (2 x + 3)
= 2( ) + 3
= 2(2 x + 3) + 3
= 4 x + 6 + 3
= 4 x + 9
This is as simplified as the expression can get, so I have my answer:
( f ∘ f )( x )) = 4 x + 9
My work looks like this:
( g ∘ g )( x ) = g( g ( x ))
= −( ) 2 + 5
= −(− x 2 + 5) 2 + 5
= −( x 4 − 10 x 2 + 25) + 5
= − x 4 + 10 x 2 − 25 + 5
= − x 4 + 10 x 2 − 20
This is fully simplified, so my answer is:
( g ∘ g )( x ) = − x 4 + 10 x 2 − 20
URL: https://www.purplemath.com/modules/fcncomp3.htm
You can use the Mathway widget below to practice function composition. Try the entered exercise, or type in your own exercise. Then click the button and select "Solve the function operation" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)
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John hendrix | jul 11, 2024.
Fantasy Football season is right around the corner, and many players will start putting in more time doing their homework to see who can help them defend their crown or improve from last season. Although it isn't what it really used to be, the New Orleans Saints are still a team that could help you in some areas.
Like Saints News Network did last season , we're back to give you an early preview for the black and gold and give you some insight to consider on who you might target when your draft gets underway. We'll be sure to give you another when we get into the thick of training camp as well.
Be sure to check out the SI hub for Fantasy Football for all of your needs for your draft. Also keep in mind that the Saints have a bye week in Week 12. Here's the skinny on potential Saints Fantasy Football targets.
For starters, remember that the league changed up the special teams rules, so that should actually help revive this position a little. New Orleans comes in with a Top-10 ranked fantasy unit in this department, and actually ranked eighth last season in scoring. The sack output should hopefully go up from last year's 34, especially with the addition of Chase Young. They were strong in the turnover department last year, coming in 4th in the NFL with 29 total. They still have a formidable unit that should turn into a nice fantasy unit.
Rashid Shaheed, Derek Carr, Taysom Hill
JOHN HENDRIX
I officially started covering the New Orleans Saints & other NFL topics in 2011. My work has been featured on various outlets over the years. I worked closely with Skyhorse Publishing in Fall 2018 to update the book, Tales From the New Orleans Saints Sidelines, which filled in all Saints material from the 2013-2017 seasons. Prior to joining Saints News Network, I served as the Managing Editor of SB Nation's Canal Street Chronicles for 3.5 years, and before that with FanSided's Who Dat Dish as the Managing Editor for several years. I have also had experiences of being a freelance Saints reporter for The Sun Herald in Biloxi, MS and a contributing writer for WDSU, a local NBC TV station in New Orleans. I have appeared on a vast amount of TV and Radio shows, both nationally and locally. For tips, comments, or suggestions, please contact me at [email protected]
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Homework is work that teachers give students to complete outside of the school day. Homework is meant to provide students with practice for what was learned in school or an extension of what was done in class. Students are expected to complete the homework and return to school with the completed homework assignment.
Composing functions symbolically means you plug the formula for one function into another function, using the entire formula as the input x-value.
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