Determine whether the given equation represents y as a function of x and explain how you know.

Question

a) 16x^2-y^2=0

b) 16-lxl=4y

thank you!

Answer 1

a) 16x^2-y^2=0
y^2 = 16 x^2
y = + 4 x or y = -4x
well y is not a unique function of x. There are two possible values of y for any old x

b) 16-lxl=4y
y = 4 - |x| /4
for every value of x there is one and only one value of y

Answer 2

(a) 16x^2 = y^2
not a function, since there are two values of y for almost all of the values of x.
Fails the vertical-line test.

(b) yes. each x has a unique |x|.