Question

1. does the graph represent a function? explain your reasoning.

Explanation:

To determine if a graph represents a function, we use the vertical line test. The vertical line test states that if any vertical line drawn through the graph intersects the graph at more than one point, then the graph does not represent a function. For the given graph (a parabola - shaped curve opening upwards), when we draw any vertical line, it will intersect the graph at most once. This is because for every \(x\) - value (input), there is exactly one \(y\) - value (output) associated with it.

Answer:

Yes, the graph represents a function. This is because when we apply the vertical line test, any vertical line drawn will intersect the graph at most once, meaning each \(x\) - value has exactly one corresponding \(y\) - value.