Question

Consider the equation y=16-x. which of the following statements is true

a. x is a function of y, but y is not a function of x.
b. y is a function of x, but x is not a function of y.
c. both x is a function of y and y is a function of x.
d. neither x is a function of y, nor is a function of x

Answer 1

C. Both x is a function of y and y is a function of x

Explanation:

A function is a relationship which assigns to each input (from the domain) value, a unique output (from the range).

y is a function of x means x is from domain, y is from range

x is a function of y means y is from domain, x is from range

1. Given
`y=16-x`

y is a function of x because for each x there is exactly one y corresponding to this x.

2. Rewrite
`y=16-x` expressing x in terms of y:

`y-16=-x\\ \\-x=y-16\\ \\x=16-y`

x is a function of y because for each y there is exactly one x corresponding to this x.