Question

I need help asap!!!

The graph of a relation is shown.
The inputs are x €____________ (Enter your answer in interval notation)
The outputs are y €____________ (Enter your answer in interval notation)
is the relation a function of x?
yes or no ​

Answer 1

Answers in bold:

inputs = [-5, 4]

outputs = [-1, 1]

Is it a function? yes

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Step-by-step explanation:

The domain is the set of allowed x inputs.

The left most point is when x = -5. The right most point happens when x = 4

We can say that "x is between -5 and 4, including both endpoints".

As an inequality, we write the domain to be
`-5 \le \text{x} \le 4` and that condenses down to the interval notation [-5, 4]

Use square brackets to include both endpoints.

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The range is the set of allowed y outputs.

The lowest we can go is y = -1, while the highest point occurs when y = 1

Therefore the range is
`-1 \le y \le 1` and that condenses down into the interval notation [-1, 1]

Both endpoints are included.

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Is this relation a function? yes it is

Why? Because each x input in the domain leads to one and only one y output in the range.

The graph passes the vertical line test. This is a test where we try to draw a vertical line passing through more than one point on the curve. But such a task is impossible. Any particular vertical line will pass through the curve at most once.

Because the graph passes the vertical line test, we have a quick visual way to see that we have a function.