Question

which of the following relations represent y as a function of x? select all that apply.
show your work here
diagram of x (a,b,c,d,e) to y (2,3,4,5,6) mapping
equation: 3y² = 9x² + 5

Explanation:

Step1: Check the mapping relation

A function requires each $x$-value maps to one $y$-value. In the diagram, every element in the $x$-set ($a,b,c,d,e$) connects to exactly one $y$-value. This satisfies the function definition.

Step2: Analyze the algebraic equation

Start with the given equation:
$$3y^2 = 9x^2 + 5$$
Solve for $y$:
$$y^2 = 3x^2 + \frac{5}{3}$$
$$y = \pm\sqrt{3x^2 + \frac{5}{3}}$$
For any single $x$-value, there are two distinct $y$-values (positive and negative square root). This violates the function definition.

Answer:

Only the mapping diagram (the left relation) represents $y$ as a function of $x$.