Question 1

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??

Accepted Answer

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

Question 2

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?

Accepted Answer

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?

Question 3

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

Accepted Answer

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?

Question 4

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?

Accepted Answer

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

Question 5

So basically -13 - (7/4b) is the same as a, which is the same as f(b). Am I right?

Accepted Answer

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.

Question 6

The practice problems are asking my to rearrange the problem so one of the variables is the independent variable but I don't understand the whole "independent" variable thing. What makes it independent? What does that even mean?

Ex: Rearrange the equation so q is the independent variable.
-7q+12r=3q-4r (that was one of the practice problems)

Ex: Rearrange the equation so q is the independent variable.
-7q+12r=3q-4r  (that was one of the practice problems)

Accepted Answer

Here is a video about independent varibles in khan academy: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-dependent-independent/v/dependent-and-independent-variables-exercise-example-1

Question 7

so technically an equation in two variables is a function and equation in one variable is just an equation

Accepted Answer

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.

Question 8

I am attempting the Function rules from Equations, but it makes so sense. For example, it gives problems like:
Rearrange the equation so x is the independent variable.
- 4 x - 6 = - 5 y - 6

That doesn't make sense at all. Actually, I know that you need to get the variable other than x on the left side (y would be the dependent variable; y's value is solely dependent on the value of x: y = __ + __x), but I don't know what to do with the other numbers. First, how do I get y on the other side? 
What do I do with the constants? Here's something that makes me more confused. In the hints, it said that you subtract them or something? Once, I had 
- 3 a + 6 b = a + 4 b + 3 a        
and it said to subtract the 4b from the 6b to get 2b, but both of those numbers are positive. Why should they be subtracted from one another?

Accepted Answer

Your 1st equation:  To isolate "y", 
1)  Add 6 to both sides
2)  Divide both sides by -5
"y" will be on the right side, but you can slip the sides of an equation: 5 = 2+3 is the same as saying 2+3 = 5

Your 2nd equation:  Remember, to move any item across the "=", you use the opposite operation.  You need to get all the "b" on the same side.  So, you subtract 4b from both sdies.

Hope this helps.

Question 9

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?

Accepted Answer

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

Algebra (all content)

Course: Algebra (all content) > Unit 7

Obtaining a function from an equation

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