👉 (of a function) Assuming each of the values in its codomain; having its range equal to its codomain.
Alright class, settle down and let’s take a look! Today we’re tackling “onto,” a word that might seem a little tricky at first glance. The dictionary gives you a mouthful – "(of a function) Assuming each of the values in its codomain; having its range equal to its codomain." Don't worry, we'll break it down piece by piece! Let’s start with the basics: “onto” means to something. Think about walking onto a stage, or putting something onto a table. It describes movement and placement. Now, when we talk about functions in math, “onto” is a bit more specific. It’s describing how a function maps things from one set (let's call it the "domain") to another (the "codomain"). Here's where that dictionary definition comes in handy: “Assuming each of the values in its codomain” : This means every single possible output value – every number you could get from the function – actually exists within the codomain. Think of it like this: if your codomain is a group of colors, and your function can create all those colors, then it’s “onto.” “Having its range equal to its codomain” : This builds on the first part! The "range" is what actually comes out of the function – the set of all possible outputs. If the range and the codomain are the same, it means every single output value is also a valid member of where those outputs can be. Let's use an example: Imagine a function that takes in numbers 1, 2, and 3 as input (that’s our domain). And let's say its codomain is the set {4, 5, 6}. If this function is “onto,” it means it can produce 4, 5, and 6. It doesn't just give you some random number – it hits every value in the codomain! Now, if a function could only output 4 and 5, it wouldn’t be "onto" because it didn’t reach all the possible outputs (the codomain). Think of it like this: A function “onto” is one that covers its entire destination. It doesn't leave any gaps! Does that make sense? Do you have any questions about what "onto" means in the context of functions, or would you like me to give you another example?