Respuesta :
Hi student, let me help you out! :)
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We are asked to describe the graph shown in the attached picture.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Please see below! ^^
Is the graph a function?
[tex]\boxed{\mathrm{Yes}}[/tex] ⇒ It passes the Vertical Line Test (Draw a vertical line through the graph; if the line touches the graph once (only once), then the graph is a function.
[tex]\boxed{\mathrm{No}}[/tex] ⇒ It doesn't pass the Vertical line test. The line touches the graph more than once.
[tex]\underline{\rule{50}{1}}[/tex]
Since the line touches the graph only once, this graph is a function, and Option A. is not right; we can cross it out.
One down, three to go! ^^
Is the graph a one-to-one function?
[tex]\boxed{\mathrm{Yes}}[/tex] ⇒ It passes the horizontal line test; it touches the graph only once.
[tex]\boxed{\mathrm{No}}[/tex] ⇒ It doesn't pass the test; the line touches the graph
[tex]\underline{\rule{50}{1}}[/tex]
Since a horizontal line touches the graph more than once, this function is not one-to-one.
Option B. isn't right either.
Two down, two to go! ^^
However, look what Option C. is. The graph we're given is indeed a function, and it's not one-to-one.
So I choose Option C.
Let's ensure our answer is correct by checking the last option:
Is the graph a linear function?
[tex]\boxed{\mathrm{Yes}}[/tex] ⇒ Its graph is a straight line.
[tex]\boxed{\mathrm{No}}[/tex] ⇒ Its graph isn't a straight line.
[tex]\underline{\rule{50}{1}}[/tex]
As we can see, the given graph is not a staight line; thus, Option D. is also wrong.
Thus, Option C. is the correct answer.
Hope it helps you out! :)
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
