Question

9

Is the function shown in the
graph one-to-one?
Yes, there exists one
input for every output.
No, there exists
more than one output for at
least one input.
• No, there exists
more than
one input for at least one
output.
Yes, there exists one output for
every input.

Answer 1

Answer: Choice D

Yes, there exists one output for every input.

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Step-by-step explanation:

x = input

y = output

For any given x value, we have exactly one and only one y value that pairs up with it. Use the vertical line test. This is where we try to draw a single vertical line through more than one point on the curve. You'll find that no such line can be drawn. Any vertical line only crosses the curve exactly once (corresponding to exactly one output). We say that it passes the vertical line test, and therefore we have a function.

Side note: the curve does not pass the horizontal line test. That means the function is not one-to-one.

Answer 2

Yes, the function is one-to-one because there exists one output for every input. Hence, the correct option is (D).

A function is said to be one-to-one if output never repeats . This means that every input value would have a unique output value.

From the graph given, each x - value(input) has a unique y-value (output) .

Hence, we can conclude that the graphed function is one-to-one.