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## 8th grade

### Course: 8th grade > Unit 3

Lesson 8: Functions- What is a function?
- Worked example: Evaluating functions from equation
- Function notation example
- Evaluate functions
- Worked example: Evaluating functions from graph
- Evaluate functions from their graph
- Equations vs. functions
- Manipulating formulas: temperature
- Obtaining a function from an equation
- Function rules from equations

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# Function notation example

Sal uses function notation to help Frank figure out how much water he can put in his balloon. Created by Sal Khan.

## Want to join the conversation?

- At1:53don't you multiply each of the terms by three to get 4 as a whole number, not divide?(7 votes)
- no because you would have to multiply the other side too and if you did that you would get the wrong answer(4 votes)

- why did he divide 27 by 3 at1:47instead of 4 divided by 3?(11 votes)
- You are free to do it in which ever order is easier for you (as long as you observe PEDMAS).

In this example we have 3³=27 and 4/3.

If you did 4/3 first, then you would have to work with 1.33333333333 (inaccurate), or the mixed fraction "1 and 1/3" and multiply those by 27.

So now you have to multiply 27 by 1.33333333333 or "1 and 1/3" that to get the answer. Can you do that in your head?

Sal noticed that 27 is divisible by 3, that is 3x9=27, and with that he can simplify the expression by removing a factor of 3 from the 3 in 4/3 and 27 to get 4 and 9 to get 36 - easy to do in your head.

You also could have taken the factor of 3 out of 3³ and 4/3, to get 3² and 4 to get 9 and 4 to get 36 - also easy to do in your head.

So you can do it in the order that is easiest for you - the goal is always to reduce careless errors.(17 votes)

- besides just water balloons, where does function notation come in handy?(7 votes)
- Function notation in maths is analogous to the list of ingredients you get given in a recipe. It won't tell you how to make the cake but it will tell you what ingredients you'll need to get when you go shopping! It's used practically in physics, and is one of the key elements in computer programming. It's particularly useful when you're looking at messy relationships with multiple variables. as it provides a quick idea of which variables are important in determining something's value.(8 votes)

- How do you compute the area of a rectangle as a function of it's width given its perimeter.(5 votes)
- Let w denote the width and h the height of the rectangle in question. Given the perimeter P, we may write P = 2w + 2h. Hence h = P/2 - w. The area as a function of its width is then given by

A(w) = wh = w(P/2 - w).(8 votes)

- I'm not sure if I'm right...

So since this is a function, would the radius be the input/domain?(8 votes) - hi, can someone help me with this problem I got? I don't know why my answer was wrong.

f(x)=-x-4. find f(-4)

the answer options were

a.0 (this was the correct answer)

b.-8 (this was the answer I got)

c. 4

d. 8(4 votes)- In this case, you would simply need to plug in -4 into the equation. So, f(-4)=-(-4)-4. This equals zero because you have a negative times -4, which equals positive 4. Then, you subtract 4, which equals 0! I think you forgot about the negative. Let me know if this helps!(6 votes)

- I need help with evaluating functions(5 votes)
- Why do you not also multiply Pi in 4/3 Pi r cubed. When the answer of the question gets to 4/3 Pi 27, why do you not have to multiply Pi with 27 and 4/3 in the problem. Is the problem solving for Pi(4 votes)
- Pi is an irrational number, and thus cannot be solved for all the way- It goes on forever without a pattern and cannot be represented as a fraction. The answer is impossible to get without rounding (inaccurate) or leaving the pi out. Thus, in order to avoid confusing the watcher by providing a non-simple or incorrect number, he chose not to multiply pi into the other values.(2 votes)

- At2:08, why doesn't Sal solve 36(3.14)? Why does he leave it as 36Pi?(4 votes)
- Well, pi is a number that goes on and on and in that case, we won't be able to get the exact number for pi. So, using 36pi would be more exact than using 36(3.14).(2 votes)

- Why did he randomly divide by 3 at1:50? What rule is that? Maybe I'm missing a subject/video where he went over these equations in more depth because he doesn't elaborate much here(2 votes)
- He just simplified the expression. We have 27/3. How many times does 3 go into 27? From your tables, you know that 9 x 3 = 27. So, 27/3 = 9. This is the same idea he applied here. He cancelled 3 and got 1 (as 3 goes into 3 1 time) and cancelled 27 and got 9 (as 3 goes into 27 9 times)

Alternatively, you can just divide the numerator and denominator by 3. You'll get (27/3)/(3/3). The numerator becomes 9 and denominator becomes 1. So, you get 9/1 = 9(3 votes)

## Video transcript

Frank wants to fill
up a spherical water balloon with as much
water as possible. The balloons he
bought can stretch to a radius of 3
inches-- not too big. If the volume of a sphere
is-- and this is volume as a function of radius--
is equal to 4/3 pi r cubed, what volume of water
in cubic inches can Frank put into the balloon? So this function
definition is going-- if you give it a
radius in inches, it's going to produce a
volume in cubic inches. So let's rewrite it. Volume as a function of radius
is equal to 4/3 pi r cubed. Now, they say the
balloons he bought can stretch to a
radius of 3 inches. So let's think about, if the
radius gets to 3 inches, what the volume of that
balloon is going to be. So we essentially would
just input 3 inches into our function definition. So everywhere where we see an
r, we would replace it with a 3. So we could write--
and just to be clear, let me rewrite it
in the same color. V of-- that's not
the same color. We do it in that brownish
color right over here. So V of 3 is equal to 4/3
pi-- and instead of r cubed, I would write 3
cubed-- 4/3 pi 3 cubed. This is how the function
definition works. Whatever we input
here, it will replace the r in the expression. So V of 3 is going to
be equal to-- so this is going to be equal to 4/3 pi
times-- 3 to the third power is 27. 27 divided by 3 is
9, so this is 9. 9 times 4 is 36 pi. So this is equal to 36 pi. And since this was
in inches, our volume is going to be in inches
cubed or cubic inches. So that's the volume
of water that Frank can put in the balloon--
36 pi cubic inches.