Question

Decide whether y is a function of x.

18. 5x-y=10

19. x^2+y^2=4

Answer 1

Question22945

Decide whether y is a function of x.

18. 5x-y=10

19. $x^{2} + y^{2} = 4$

**Solution.**

By the definition $f$ is a function for every $x \in X$ there is exactly one element y such that the ordered pair $(x, y)$ is contained in the subset defining $f$.

18. Consider the relation $5x - y = 10$. It is clear that for each real number $x$ there is the unique $y = 5x - 10$ such that $f(x) = y$.

19. The relation $x^{2} + y^{2} = 4$ is not a function as for the element $x = 1$ there are two points $y_{1} = \sqrt{4 - x^{2}} = \sqrt{3}$ and $y_{2} = -\sqrt{4 - x^{2}} = -\sqrt{3}$ such that $y = f(x)$

**Answer.** $5x - y = 10$ is a function, $x^{2} + y^{2} = 4$ is not a function.