Determine whether each function graphed or defined is one-to-one....

Question

Determine whether each function graphed or defined is one-to-one.

Graph of a function showing a curve that is not one-to-one.

Accepted Answer

Hey, everyone in this problem, we're asked to identify whether the given graph is a 1 to 1 function or not. Now, the graph we're given has a function. It's increasing, it looks exponential and it's increasing from around negative six in the X axis up to about four in the X axis. And it increases up to a value of around 10 at the X value of six. We're given two answer choices. Option A yes or option B no. So let's recall, OK. A 1 to 1 function. And sometimes these are also called injective function. So you may have seen that in your course or in your textbook and this is a function where each Y value only has one corresponding X value. So what we want to do when we have a graph to test if it's a 1 to 1 function is to look at the horizontal line test. So we're gonna draw horizontal lines on our graph and we're gonna see how many points they intersect that graph and we can draw these horizontal lines anywhere along this curve. And we see that there's only one intersection point, OK. Every time we draw a horizontal line, it only intersects our graph once that means that we pass the horizontal line test that gets a green check mark. So we passed the horizontal line test. OK. Each Y value only has one corresponding X value. And so this is indeed a 1 to 1 function. So the answer choice here is option A, this is a 1 to 1 function. It passes that horizontal line test. Thanks everyone for watching. I hope this video helped you in the next one.

Determine whether each function graphed or defined is one-to-one.

Key Concepts

One-to-One Function

Horizontal Line Test

Graph Interpretation

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