select all of the following graphs which represent $y$ as a function of $x$. (hint: use the vertical line…

select all of the following graphs which represent $y$ as a function of $x$. (hint: use the vertical line test.)\nquestion help: video written example message instructor

select all of the following graphs which represent $y$ as a function of $x$. (hint: use the vertical line test.)\nquestion help: video written example message instructor

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: Evaluate top-left graph

Any vertical line intersects this graph at most once. It passes the test.

Step3: Evaluate top-right graph

A vertical line (e.g., $x=-1$) intersects the circle twice. It fails the test.

Step4: Evaluate middle-left graph

Any vertical line intersects this graph at most once. It passes the test.

Step5: Evaluate middle-right graph

Any vertical line intersects this horizontal line exactly once. It passes the test.

Step6: Evaluate bottom-left graph

Any vertical line intersects this graph at most once. It passes the test.

Step7: Evaluate bottom-right graph

Any vertical line intersects this line exactly once. It passes the test.

Answer:

  • Top-left graph (the curved graph crossing the origin)
  • Middle-left graph (the wave-like graph)
  • Middle-right graph (the horizontal line $y=2$)
  • Bottom-left graph (the narrow U-shaped/zig-zag graph)
  • Bottom-right graph (the positive-sloped straight line)