Question

Which of the following are functions?

Options

• (a) {(x, y) : y² = x, x, y ∈ R}

• (b) {(x, y) : y = |x|, x, y ∈ R}

• (c) {(x, y) : x² + y² = 1, x, y ∈ R}

• (d) {(x, y) : x² − y² = 1, x, y ∈ R}

   

Answer 1

(b) {(x, y) : y = |x|, x, y ∈ R}

For every value of x ∈ R, there is a unique value y∈ R.
i.e. there is a unique image for all values of x ∈ R.
Also, values of x occur only once in the ordered pairs.
Thus, it is a function.