Question

select all of the following graphs which represent ( y ) as a function of ( x ).

Explanation:

To determine if a graph represents \( y \) as a function of \( x \), we use the vertical line test: a graph represents a function if no vertical line intersects the graph more than once.

Step 1: Analyze the first graph (line)

The first graph is a straight line. For any vertical line \( x = a \) (where \( a \) is a real number), the line will intersect the graph at exactly one point. So, it passes the vertical line test.

Step 2: Analyze the second graph (wave)

The second graph is a wave - like curve. For any vertical line \( x = a \), this curve will intersect the vertical line at most once. So, it passes the vertical line test.

Step 3: Analyze the third graph (ellipse)

The third graph is an ellipse. If we draw a vertical line through the ellipse (for example, a vertical line that passes through the major or minor axis of the ellipse), it will intersect the ellipse at two points. So, it fails the vertical line test.

Step 4: Analyze the fourth graph (vertical line - like)

The fourth graph has a part that is a vertical line (or a very steep line that is almost vertical). A vertical line \( x = a \) (where \( a \) is the \( x \) - value of this vertical part) will intersect this graph at more than one point. So, it fails the vertical line test.

Answer:

The first graph (the straight line) and the second graph (the wave - like curve) represent \( y \) as a function of \( x \).