Math Problem Statement
Is this a function and a one-one function? what is the domain and range?
Solution
From the image, we can observe a red curve plotted on a coordinate plane. Let's address your questions one by one:
1. Is it a function?
Yes, the curve shown represents a function. A function passes the vertical line test, which states that if any vertical line intersects the graph at more than one point, it is not a function. In this case, every vertical line intersects the curve at only one point, so it satisfies the condition to be a function.
2. Is it a one-to-one function?
No, it is not a one-to-one function. A one-to-one function passes the horizontal line test, which means that any horizontal line should intersect the graph at most once. In the given graph, there are horizontal lines (e.g., around ) that intersect the curve at more than one point, so the function is not one-to-one.
3. What is the domain?
The domain of a function refers to all the possible values of (input values) for which the function is defined. From the graph, it appears that the curve extends indefinitely to the left and right, meaning the domain is:
4. What is the range?
The range of a function refers to all the possible values of (output values). Observing the graph, the lowest point seems to be around , and the highest point goes up beyond . Therefore, the range is approximately: since the curve seems to extend vertically in both directions without bound.
Would you like a more detailed explanation or further clarification?
Here are 5 related questions you might find interesting:
- How can you algebraically check if a function is one-to-one?
- What is the significance of a function's domain and range in real-world applications?
- Can a function be many-to-one and still be considered a function?
- How does the concept of injectivity relate to one-to-one functions?
- What are examples of functions that are not one-to-one but are still widely used?
Tip: If you're unsure whether a function is one-to-one, always apply both the vertical and horizontal line tests!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Functions
One-to-One Functions
Domain and Range
Formulas
Vertical Line Test
Horizontal Line Test
Theorems
Vertical Line Test for Functions
Horizontal Line Test for One-to-One Functions
Suitable Grade Level
Grades 9-12