Answer:
It is a many-to-one function ⇒ answer B
Step-by-step explanation:
* <em>To solve this problem lets revise some important notes</em>
- <u>We use the vertical line to check the graph is function or not</u>
# If the vertical line cuts the graph in any part of it in <em>only 1 point</em>
then the graph represents a <em>function</em>
# If the vertical line cuts the graph in any part of it in <em>more than 1 </em>
<em> point</em> then the graph <em>doesn't</em> represent a <em>function</em>
- <u>We use the horizontal line to check the graph is one-to-one function</u>
<u>or many-to-one function</u>
# If the horizontal line cuts the graph in any part of it in <em>only 1 point</em>
then the graph represents <em>one-to-one</em> <em>function</em>
# If the horizontal line cuts the graph in any part of it in more than 1
point then the graph represents <em>many-to-one function</em>
* <em>Now lets use these notes to solve the problem</em>
- <u>Look to the attached graph</u>
∵ The vertical lines x = -2 and x = 2 intersect the graph of f(x) in
only one point
∵ Any vertical line will cut the graph of f(x) in only one point
∴ <em>f(x) is a function</em>
- So answers <em>A and C</em> are <em>not true</em>, because it succeeds the vertical
line test and it is a function
∵ The horizontal lines y = -4, y = 4, and y = 11 intersect the graph of f(x)
in more the one point one point
∴ <em>f(x) is many-to-one function</em>
- So answer <em>D</em> is <em>not true</em>, because f(x) is many-to-one function
∴ <em>Answer B is true because f(x) is many-to-one function</em>