I had a question on a quiz that I just finished and I wanted to know if my answer was right.

Is 4x-y^=0 a function. If so, what is the domain and range? If not, name two points that prove it.

I wrote that it was a function with -5 and lower as a restriction and
Domain (-5, infinity)
Range (- infinity, infinity)

written as 4x = y^2, you should realize that you have a parabola, with its axis of symmetry the x-axis, vertex as (0,0), opening to the right.

domain: x ≥ 0
range : any real number

btw, it is not a function

e.g. both (4,4) and (4,-4) lie on it, so we have 2 different y values for the same x, which is a violation of the definition of a function.

To determine if the equation 4x - y^2 = 0 is a function, we need to check if each x-value corresponds to a unique y-value.

First, let's solve the equation for y to get it in terms of x:
4x - y^2 = 0
=> y^2 = 4x
=> y = ±√(4x)

Since we have a ± sign, this suggests that there are two possible y-values for each x-value. Consequently, the equation is not a function.

To prove this, we can provide two points that have the same x-value but different y-values. Let's choose x = 1:
y = ±√(4 * 1)
y = ±√4
y = ±2

So, the two points are (1, 2) and (1, -2). Both points satisfy the equation, but they have different y-values, indicating that the equation is not a function.

Now, let's determine the domain and range.

The domain refers to all the possible x-values for which the equation is defined. Since there is no restriction on the x-values in the equation, the domain is all real numbers (-∞, ∞).

The range refers to all the possible y-values that correspond to the defined x-values. Since we can have any positive or negative value for y, the range is also all real numbers (-∞, ∞).

Therefore, your answer for the domain and range is correct:
Domain: (-∞, ∞)
Range: (-∞, ∞)