Answer: Yes to all 3 questions
- It is a function.
- The function is one-to-one.
- The function has an inverse, which is also a function.
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Step-by-step explanation:
VLT = vertical line test
HLT = horizontal line test
The given curve passes the VLT since it's not possible to draw a single vertical line through more than one point on the blue curve. Therefore, we have a function. Any input (x) leads to exactly one output (y).
The curve also passes the HLT through similar reasoning (use a horizontal line this time of course). This tells us the function is one-to-one. Each input leads to a unique output.
The keyword "unique" is important in the previous paragraph. It's needed to help set up the inverse. Since this curve passes the HLT, we know the inverse exists and it is a function. The inverse itself will pass the VLT.
Note: recall you reflect the given curve over the line y = x to form the inverse curve.