Determine whether each relation defines a function, and give t...

Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

Accepted Answer

Hello, everyone. We're gonna identify if the graph we're given is a function and also find the domain and the range. So the first thing I recall about a function when I'm looking at a graph is that I can use what we call a vertical line test, meaning I can make a vertical line. And if it only passes through the graph once, then it is a function. So I'm going to do that a couple of times verticals up and down and passes through once here and I'm going to check over here. Yep, still only passing through the graph once. So based on the picture we're given this is a function. So now I need to decide what the domain and range are, the domain is going to be all of the X values that are covered by this graph. So looking at my graph, it has arrows at the end, I'm gonna move these lines out of the way so we can see them. So those arrows at the end meaning it goes on infinitely. Um And it looks like if you think about it in terms of left and right, it continues going left and right forever. So our domain is gonna be all real numbers. So negative infinity to positive infinity, the range is when we look at the Y values. And so are there any y values here that aren't covered? Well? Yes, it looks like it never goes above this point here. So that means all of our y values are less than -2. So if everything is less than negative two, that means it goes from negative infinity two, negative two, But it does include -2. So it will be a bracket. So our domain is all real numbers, Our range is negative infinity to -2 including -2. And that would be answer choice B have a nice day.

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

Key Concepts

Definition of a Function

Domain of a Relation

Range of a Relation

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