Final answer:
The equation y^2 = x + 3 is not considered a function because for any given x there can be two different y values. In contrast, y = 9 + 3x is a valid function with a unique y for every x.
Step-by-step explanation:
When evaluating whether y^2 = x + 3 is a function, we apply the definition of a function as a relation where each input (value of x) corresponds to exactly one output (value of y). However, this equation does not represent a function because for a given value of x, there can be two different y values, one positive and one negative, since y is squared. To illustrate a function, let's consider the equation y = 9 + 3x. This is a linear function with a slope (m) of 3 and a y-intercept (b) of 9. To verify its functionality, we can create a value table or plot it on a graph, making sure that for each x-value, there is only one corresponding y-value.