Determine if the equation represents y as a function of x. Justify your answer. 3x^2+2y=17

Question

college algebra assignment, work needs to be shown

Answer 1

y is a function of x

3x^2 + 2y = 17

Rewrite solving for y

2y = -3x^2 + 17

divide by 2

y = (-3/2)x^2 + 17 is a dowwnward opening parabola with vertex (0,17)

it passes the vertical line test. It's impossible to draw a vertical line through the vertical parabola and cut it more than once, So it's a function.

Not a one-to-one function though, as it fails the horizontal line test