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# 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.

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• 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?
• 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
• You solve for a because a is the output or in other words a is the f(B). I think this is right. Any other ideas?
• 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.
• 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?
• Me too! I don´t understand this lesson. 6th grader
(1 vote)
• 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?
(1 vote)
• Look at the second line:
a=3(b+2)+7 ---> a=3*b+3*2+7 ---> a=3b+6+7 ----> a=3b+13
That is how you get 13!
Greetings,
Pedro
• 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.
• What? why are we solving for a? why not b? where is the input for the function here? what does solving for a have to do with this f(b). How is f outputting a? im so confused
• If the problem is asking you to create function f(b), then it is telling you that the input value is defined by "b", not "a". So, "a" becomes the variable that you isolate and switch to f(b).

If you solved for "b", then the input value would need to be "a" and the problem didn't ask you to create f(a).

Hope this helps.
• this is really hard
• By now, you should have experience solving equations for "y" to change a linear equation into slope-intercept form. Use those skills.

The 1st step is to solve the equation for "y" (isolate "y" by itself on one side of the equation.

The 2nd step is to replace "y" with f(x), or whatever name you were asked to use for your function.

Hope this helps.