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### Course: Integrated math 3>Unit 7

Lesson 6: Solving equations by graphing

# Solving equations by graphing

You probably already solved a system of equations by graphing the equations and looking for intersection points. This method can actually be used to solve (or find an approximate solution to) any single equation, no matter what kind! This is a very exciting tool.

## Want to join the conversation?

• Are there tools in the future courses that will allow me to solve a problem like this?
That is without doing it using brute force and let the computer graph the functions for me.
• The tools needed to solve this equation algebraically aren't on Khan Academy. This equation can only be solved in terms of something called the Lambert W function, which is only presented in some college math courses.

However, Khan Academy will provide better tools to approximate the solution by hand in the calculus section.
• Can someone give me a basic review on functions like what it means by putting in a impute to get an output?
• Imagine you have a machine (call that a function) that, when fed with something, spits something else out.
This machine follows the rules:
* Take the name of a person
* Give the name of the biological mother of that person
So, if I input myself, I would get as an answer my mother.
In this case, the person's name is the input, the mother's name is the output and the machine is the function.
Now let's try it with numbers.
Say we have a machine (function) that takes any number and doubles it. We can represent that as f(x) = 2x (reads "f of x equals two x"). That means that, when we input any x into f(x), our answer is going to be 2 times that x. f(2) = 2*2 = 4.
The input is simply the x I chose (in this case 2) and the output was what the function spat out (in this case, 4).
And we can do more complicated functions, like:
f(x) = x²
What this function tells us is to square any number that we input into the function.

Things that are important about functions:
A function can only be a function if it has only one output per input. What this means is, if I input a number, the answer should always be only that one output. f(x)=2x can never give different results for the same x. By consequence, f(x) = +/-√x is not a function, because the square root of 4 can be either 2 or -2.
We can also always graph a function, denoting the y-axis as f(x). What this means is that, for every x in the x-axis, we input that into the function we're graphing, and the result is going to be the y-coordinate of that x.

I hope that helped a little bit. Not only you, but other people that may read this comment.
• “pause this video and see if you can solve this” farewell my last remaining brain cell, you will be missed