Functions24.1 For each of the following relations; determine whether or not it is function. Please explain YOnr answers. And if it is a function, what are its domai...

Determine whether each relation is a function. Give the domain and range for each relation. a. $\{(1,6),(1,7),(1,8)\}$ b. $\{(6,1),(7,1),(8,1)\}$ (Section $1.2,$ Example 2 )

We need to determine the following is a function or not function. If it's a function then we need to find the domain and range. So here we look at our X values, our X values don't repeat. So this is a function. So our domain consists of um X. Is such that X Equals 2 to the end power or mm numbers of N. And or why? Or is our ranges? Why is such that? Why is any whole number?

Okay, so here's a quick sketch of our picture passes through one and one. The first question is to find the domain. Since there are no restrictions here, there's no there, no holes. There's no acid totes. There's nothing to break this up. If I put my pencil on the function and I went from all the way to the left all the way to the right, my domain would be all rial numbers, and the best notation is interval notations. We would say it's from negative infinity to positive infinity. You can also use the all rial number. First symbol the range. If we go from the bottom all the way to the top again, every single why value can be achieved. So again, it's all riel numbers again. Best notation interval notation Negative infinity to positive in minutes. Not a point. It's for start to finish. Um, again, we could also use all real numbers and because each input gives you exactly one output, this is indeed a fat. In fact, a function

Okay, so we're dealing with in a lips here where the highest values and the lowest values to the right into the left would be positive and negative. Three in the highest and lowest values, up and down would be negative. Two and positive, too. Notice that the graft doesn't go anywhere to the left of negative three and doesn't go anywhere to the right of positive. Three. Therefore, the domain is X is an element of, and we like to always say that it's actually we know which variable we're talking about. X goes from negative three to positive three. Right? This is interval notation. If you want to use inequality notation, we would say negative three is less than or equal to X, which is less than or equal to three. Either one of these notations would be fine for domain. We talk about range. Why is an element and it goes from negative to on the low end to positive two on the high end again, we could also say that it's negative. Two is less than or equal to why, which is less than or equal to two. The question is whether it's a function or not, And the answer is not a function, and the reason it's not a function is because there are multiple X values that have that have a an output. The definition of a function is each input must have exactly one output, and, for example, it fails right here at one, for example, where one has chewed different outputs does not function.

Okay, so we're looking at this nice pretty parabola that has a vertex at zero negative one right down here. Zero negative one. And we talk about the domain we're talking about. Left to right. Notice that the arrows keep going. Every X value to the left will have an output value. Every X to the right will have an open value. In fact, there's no X value that will not have an Al Qaeda ties. So the domain acts would be an element from negative infinity to infinity. That's interval notation. We could also say that X is an element of the rial numbers. It means it's all real numbers. They're possible. The range, however, has is restricted. Notice that I can get it, or why value for everything above negative one, but nothing below negative one. So we would say that why is an element from negative one inclusive? That's always the bracket up to infinity. Otherwise, we could also write this as why is greater than or equal to negative want. This all depends on your teachers preference for notation. I personally like interval notation, but all teachers are a little bit different. So finally, is it a function. Every X value goes toe on Lee one y value. Throughout this entire graph, there's no X value that goes to two different places. So, yes, it is a function.