Question

select all of the following graphs which represent y as a function of x. question help: message instructor submit question

Explanation:

To determine if a graph represents \(y\) as a function of \(x\), use the Vertical Line Test: any vertical line drawn on the graph should intersect the curve at most once.

1. Top-left empty grid: No curve, so it trivially satisfies the test (no \(x\) has multiple \(y\) values).
2. Top-right line: All vertical lines intersect the line exactly once, passes the test.
3. Middle-left circle: A vertical line through the circle will intersect it twice, fails the test.
4. Middle-right wave: All vertical lines intersect the wave at most once, passes the test.
5. Bottom-left curve: All vertical lines intersect the curve at most once, passes the test.
6. Bottom-right S-shaped curve: A vertical line through the overlapping region will intersect twice, fails the test.

Answer:

• Top-left empty graph (the first grid with no curve)
• Top-right linear graph (the downward-sloping line)
• Middle-right wave graph (the oscillating curve)
• Bottom-left polynomial graph (the curve with two turning points)