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### 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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# Worked example: Evaluating functions from equation

Learn how to evaluate f(x)=49-x² at x=5. Created by Sal Khan.

## Want to join the conversation?

- Can anybody help me find the output, k, when the input, t, is −7.

k = 10t-19

k = ?

I need a hand. Thank you(20 votes)- You just neet to replace "t" with the given value "-7"

k = 10(-7)-19

Then, follow order of operations rules to calculate the value of "k".

Give it a try. Comment back if you get stuck or have questions.(33 votes)

- 1. Can a function have name like add(x) instead of f(x)?

2. Can a function have more than 1 argument, like f(a, b, c)?

3. Can a function's argument have a name like "apes", "apples" instead of "x", "y"?(10 votes)- 1. Yes. In mathematics it is more common to use a single letter (sometimes a Greek letter), but a function name can be anything. After all it's just a way to communicate to other humans what you're talking about, changing a name doesn't change the math.

2. Yes. A simple example is f(x,y) = x * y.

3. Yes. See answer 1: single letter names are conventional, but not required. They're all just names. You could even draw pictures instead of using letters - in fact, Khan Academy does that in some early math videos.(19 votes)

- What are the general rules for solving functions?(4 votes)
- like terms should ALWAYS be combined, that's one thing you can keep in mind(14 votes)

- Can Someone Help Me Solve This Function?

f(0)^2

where f(x)=3x+4(7 votes)- Find f(0): f(0) = 3(0) + 4

Once you know, f(0), square the result.(7 votes)

- does anyone know how to do this?(10 votes)
- How do you know where the output is?(9 votes)
- To get the output (or know where it is) you have to solve the equation for y (y is the output). So to graph it you'll use the input as the x coordinate and the output as the y coordinate.(0 votes)

- why not just put the number there instead of using functions?(5 votes)
- Nice question. There's nothing wrong with doing that, of course!

However, with function notation, specifying the input (`x`

) value is much easier.

As you know,`y = 4x + 2`

and`f(x) = 4x + 2`

are the same.`y`

and`f(x)`

are**interchangeable**.

To show how they're both evaluated at`x = 3`

:

-`x = 3: y = 4(3) + 2 = 14`

-`f(3) = 4(3) + 2 = 14`

Instead of specifying that`x = 3`

then writing the substituted`y`

equation, you can just say`f(3)`

, which implies that`x = 3`

(as the`3`

is in place of`x`

) and plugged into the function.

In this way, among others, function notation is advantageous compared to the`y=`

notation! It makes the*working out*much clearer, and thinking of things as a function can really help with certain math problems later on.

Happy learning.(2 votes)

- So the "f" in f(x) stands for function? As in solve the function with whatever the x variable may be?(3 votes)
- That's not quite right, it's more accurate to say that "f" is the name of the function. You can name a function whatever you want, but f is just the most common one people use.

You're right otherwise. If you see f(5), you just evaluate with x=5.(5 votes)

- I love functions! They are so interesting and fun to solve!(4 votes)
- Wouldn't the answer be 25 cause a neg. times a neg is 25?(3 votes)
- Yes, since a negative number squared is also positive.(1 vote)

## Video transcript

The function f of
x is defined as f of x is equal to
49 minus x squared. Find the value of f of 5. So whenever you're
dealing with a function, you take your input. In this case, our input
is going to be our 5. We input it into our
little function box, and we need to get our output. And they defined the
function box here as whatever your input is,
take that, square it, and then subtract it from 49. So f of 5, every time I
see an x here, since f of x is equal to this,
every time I see an x, I would replace
it with the input. So f of 5 is going
to be equal to 49 minus-- instead of
writing x squared, I would write 5 squared. So this is equal to 49 minus 25. And 49 minus 25 is equal to 24. And we are done.