Solve for y in terms of x . Determine if y is a function of x . If it is, rewrite using notation and determine the domain.
xsquared+12x-3y+9=0
is it
xsquared + 12x +9=3y
f(x)=xsquared + 12x + 6=y ?
no, should be
y = (1/3)x^2 + 4x + 3
(each term had to be divided by 3)
and yes, it is a function whose domain is the set of real numbers
y=x^2+12x+6
Now, is y a function of x?
What is the domain of x?
please disregard
Y=5+-6
y=7+-6X=2
7+=-6=4
y=8-6=8+4=12
SO THE APPLICATION OF X IS ABOUT TO MOVE EXACTLY WERE IT IS AND NEGATIVELY MOVE TO THE POSITIVE NUMBER SO THE ANSWER IS
NEGATIVE 12
To solve for y in terms of x, we need to isolate the y variable on one side of the equation. Let's start by rearranging the equation given:
x^2 + 12x - 3y + 9 = 0
First, move the constant term to the right side of the equation:
x^2 + 12x - 3y = -9
Next, isolate the y variable by subtracting 12x from both sides:
-3y = -x^2 - 12x - 9
Now, divide both sides by -3 to solve for y:
y = (1/3)(x^2 + 12x + 9)
Now that we have solved for y in terms of x, we can determine if y is a function of x. In this case, since each value of x corresponds to a unique value of y, y is indeed a function of x.
To rewrite the equation using function notation, we can use f(x) as the function name:
f(x) = (1/3)(x^2 + 12x + 9)
The domain of the function can be determined by considering the values of x that make the equation valid. In this case, since x can take any real number value, the domain is all real numbers.