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: Recall the vertical line test
A graph represents (y) as a function of (x) if and only if no vertical line intersects the graph more than once.
Step2: Analyze each graph
- First graph:
- For any vertical line (x = a), it intersects the graph at most once.
- Second graph:
- For any vertical line (x = a), it intersects the graph at most once.
- Third graph:
- For any vertical line (x = a), it intersects the graph at most once.
- Fourth graph:
- There exists a vertical line (for example, near (x = 1)) that intersects the graph more than once.
- Fifth graph:
- For any vertical line (x = a), it intersects the graph at most once.
- Sixth graph (the partial - circle at the bottom):
- A vertical line (x=a) (where (a) is in the domain of the circle part) intersects the graph more than once.
Answer:
The first, second, third, and fifth graphs.