were suppose to see if its a function or not and i don't get these problems can you explain it to me?
1) X=15
2) y=3x+2y
If there is one and only one value for the dependent variable in the domain then it is a function.
x = 15 is not a function because there are an infinite number of y values along the vertical line x = 15
however y = 3x+2y (I assume not a typo with that second y) is
y = -3x
which is a straight line with one value of y for every x. Therefore y is a function of x
if i were to graph it (question2)would it be on the negative side or positive side
Both James. That line goes from the upper left to the lower right, passing through (0,0)
yes but i still don't get how you got that (1st james)whats the coordinates
Well you wrote
y = 3x+2y
(I still wonder if it is not a typo, check the book to see if that second y term should really be just 2 and not 2y)
I subtracted y from both sides to get
0 = 3 x + y
then subtracted 3x from both sides to get
y = -3x
Now that is a straight line through the origin with a slope of -3
try several values o x
like
x = - 1, then y = -3*-1 = 3
x = 0, then y = -3*0 = 0
x = +1, then y = -3*1 = -3
(1st james) that means to make a parabola with a slope of -3
It is a line. There is no x^2 in it so it is not a parabola.
It is of form
y = m x + b, a line
where m, the slope is -3 and b is zero.
Sure! I can help explain how to determine if each of these expressions is a function or not.
To check if an expression is a function, we need to understand the concept of a function. In mathematics, a function is a relation between two sets of values, where each input value (x) is mapped to exactly one output value (y).
Let's take a look at each expression:
1) X = 15
In this case, we have a single equation with only one variable, X. Since X is not related to any other variable or equation, this expression is considered a function. It states that for any value of X, the output value will always be 15.
2) y = 3x + 2y
In this expression, we have two variables, x and y. To determine if it is a function or not, we need to examine the relationship between the variables. If we rearrange the equation, we get:
2y = 3x + y
Now let's isolate y:
2y - y = 3x
Simplifying, we get:
y = 3x
Now notice that for any given value of x, we have a corresponding value of y. This means that each input value (x) is mapped to exactly one output value (y). Therefore, the expression y = 3x is a function.
To summarize, the first expression (X = 15) is a function because it only has one variable and no other relations. The second expression (y = 3x + 2y) is also a function because each input value of x corresponds to one output value of y.