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 is 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, it will intersect the line at most once. So, it passes the vertical line test.

Step 2: Analyze the second graph (curve)

The second graph is a curve (polynomial-like). For any vertical line, it intersects the curve at most once. So, it passes the vertical line test.

Step 3: Analyze the third graph (self - intersecting curve)

The third graph has a "loop" or self - intersection. A vertical line can intersect this graph more than once. So, it fails the vertical line test.

Step 4: Analyze the fourth graph (circle)

The fourth graph is a circle. A vertical line can intersect a circle at two points. So, it fails the vertical line test.

Step 5: Analyze the fifth graph (wave - like curve)

The fifth graph is a wave - like curve. For any vertical line, it intersects the curve at most once. So, it passes the vertical line test.

Step 6: Analyze the sixth graph (horizontal line)

The sixth graph is a horizontal line. For any vertical line, it intersects the horizontal line at most once. So, it passes the vertical line test.

Answer:

The graphs that represent \( y \) as a function of \( x \) are the first graph (the straight line), the second graph (the curve), the fifth graph (the wave - like curve), and the sixth graph (the horizontal line).