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## Algebra 1

### Course: Algebra 1>Unit 8

Lesson 3: Functions and equations

# Obtaining a function from an equation

Equations and functions are not the same thing, but they can be related in several ways. In this video, we obtain a function from an equation. The function represents the same relationship between the quantities in the equation.

## Want to join the conversation?

• Hi, there is this one problem in the exercise "Write function rules from equations" that I am having a hard time with. It wants me to enter the greek letter upsilon as part of the answer, but I don't know how. How can I do that?? • The input is b, so, f(b), the output is a, so f(b)=a, whatever input b we plug into our function, it's gonna output a.
Therefore, to satisfy the equation we need to solve the equation in terms of a, and then just replace the a in f(b)=a, and that's our function, bellow is a summary of the steps.
f(b)=a // whatever b we input, the function outputs a
4a+7b = -52 // this is the equation our a has to satisfy
a = -13-(7/4)*b // therefore we solve for a, so the equation stands true
f(b) = -13-(7/4)*b // we replace the a in f(b)=a with whatever a equals to
• I am doing the exercises now but I haven't gotten a single one right. I don't think Sal gave an adequate enough explanation. He only did a couple examples and when I look at the hints they seem lazy and not very in depth... XD what do I do? •  So here is one of the practice problems:
7m+2=6n−5 what is f(m)?
Since the independent variable is m indicated by being in the functional parenetheses, we must solve for the dependent variable, and the only one left is n, so lets solve for n
6n - 5 = 7m + 2 just flipped sides of equation
6n = 7m + 2 + 5 moved the -5 by adding 5 on both sides
6n = 7m + 7 combined like terms
n = 7/6 m + 7/6 divided all terms by 6
f(m) = 7/6m +7/6 substituted functional notation with equation notation
Does this help?
• In school, I have a teacher that doesn't explain anything. I am a 6th grader so in Algebra 1 and I am having a lot of trouble with functions. I can solve functions but creating a linear function equation is difficult for me. Could anyone help explain it to me in an easy way that I could understand? •   In a normal linear equation you might have something like this: a = 2b + 6
You can find out what a is for any value of b by imputing the b value into the equation. For example, what is a when b is 4?
a = 2 x 4 + 6
a = 8 + 6
a = 14
In a linear function equation instead of finding a for any value of b, you find the f(b) for any value of b. You can input any value of b and get you're answer without worrying about a.
Basically, f(b) = a = 2b + 6 or f(b) = 2b + 6
• Why would you solve for A if you are trying to figure out a formula for B ? In other words trying to get B by it self. For this problem I subtracted 4a by itself and -52 which then simplified to 7b= -52-4a / 7 which simplified even more to which b = -52-4a / 7 • So basically -13 - (7/4b) is the same as a, which is the same as f(b). Am I right? • Yes, you are correct.

When f(b) is given a "b" value we get an "a" value which is the same as "f(b)".

For example if we're given the "b" value of 0, then f(0) = -13 and that is what "a" would be if "b" is zero. "f(b)" is a more concise way to say this since it says what value of "b" was used to get the "f(b)" value - to get a particular "a" value.

I hope this helps.
• I was starting to understand this until I ran into a problem on the exercises.
a - 7 = 3(b+2)

I was able to get a by itself

a = 3(b+2)+7

in the hints it said it would simplify down to

a = 3b + 13.

My question is how do you get 13? • mybrain.exe is not responding • so technically an equation in two variables is a function and equation in one variable is just an equation • Not necessarily.
A function is a relationship where each input value (X) will create only one output value (Y). Basically, a single input value, can't create 2 different output values.

Any equation with one or two variables that meet this definition would be a function.
y = 5 is the equation for a horizontal line. It is a function where all values of X have a y-value = 5. Yet it has one variable.
x = 5 is the equation for a vertical line. It is not a function because in this situation, the input value (x=5) has an infinite number of output values.
All other equations of lines (Ax + By = C) are functions because the meet the definition of a function.
But, the equation of a circle, which also uses 2 variables, would not be a function because each input value (x) creates 2 output values (y).

If an equation is not a function, sometimes we can still change it into a function if we restrict its inputs or outputs.

Hope this makes sense.  