Exercise 10

In this exercise, we want to algebraically identify when the graph of a given equation can be expressed as:

• $y$ as a function of $x$, but $x$ cannot be written as a function of $y$
• $x$ as a function of $y$, but $y$ cannot be written as a function of $x$
• $y$ as a function of $x$ and $x$ as a function of $y$
• neither $y$ as a function of $x$ nor $x$ as a function of $y$

For each equation below, state which of the four options above applies to whether the graph can be expressed with each coordinate being a function of the other or not.

1. $3x-2y=10$

2. $3x^2+2y^2=10$

3. $3y=10x^2-10$

4. $y=5$

5. $x=2$