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

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

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

Answer

Explanation:

Step1: Apply Vertical Line Test

A graph represents $y$ as a function of $x$ if no vertical line intersects the graph more than once.

Step2: Test Top Graph

Any vertical line intersects the horizontal line $y=1$ exactly once. So it is a function.

Step3: Test Middle Graph

Any vertical line intersects the diagonal line exactly once. So it is a function.

Step4: Test Bottom Graph

A vertical line (e.g., $x=-2$) intersects the ellipse twice. So it is not a function.

Answer:

The top horizontal graph and the middle diagonal graph represent $y$ as a function of $x$ (check the boxes next to these two graphs).