Question

Which of the following relations is y not a function of x?

a) y = 8x - 4
b) 8y = -4y - 8x
c) y = 8x - 4xtancos
d) y + x = 64

Answer 1

Option b (8y = -4y - 8x) is not a function of 'x'.

Step-by-step explanation:

In order for a relation to be a function, each value of 'x' in the domain must have only one corresponding value of 'y' in the range. To determine which relation is not a function of 'x', we need to analyze each option:

1. Option a: y = 8x - 4. This is a linear equation and represents a function because for every 'x' value, there is a unique 'y' value.
2. Option b: 8y = -4y - 8x. This equation does not represent a function because it can be rearranged as y = -0.5x, meaning multiple 'x' values can have the same 'y' value.
3. Option c: y = 8x - 4xtancos. This equation represents a function because there is a unique 'y' value for every 'x' value.
4. Option d: y + x = 64. This equation represents a function because it can be rearranged as y = 64 - x, meaning every 'x' value has a corresponding unique 'y' value.

Therefore, option b (8y = -4y - 8x) is not a function of 'x'.