Question

Determine whether each function is one-to-one, onto, both, or neither.

Answer 1

Answer:  Both

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Explanation:

We see that the function passes the horizontal line test. It is impossible to draw a single horizontal line and have that horizontal line cross the curve at multiple points. It's similar to the vertical line test.

Since the curve passes the horizontal line test, that makes it one-to-one. Any y value is paired with a unique x value, and vice versa.

The function is also onto because we can generate any y value output we want. The curve extends forever upward and downward. The range is the set of all real numbers.

Therefore, the function is both one-to-one and onto.

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Extra info:

• The term "injective" is the same as "one-to-one"
• The term "surjective" is the same as "onto"
• The term "bijective" is a combination of injective and surjective at the same time