Math Problem Statement

correct or no?

The given graph below is a one-to-one function.

Solution

The graph in the image depicts a curve that looks like part of a rational or logarithmic function, which is decreasing and passes the vertical line test. To determine whether this graph represents a one-to-one function, we apply the horizontal line test: if any horizontal line intersects the graph at most once, the function is one-to-one.

From the graph, it appears that no horizontal line intersects the curve more than once, so the function is one-to-one.

Therefore, the correct answer to the question is True.

Would you like further details, or do you have any questions?

Here are five related questions for you:

  1. How can you tell if a function is one-to-one using its algebraic form?
  2. What is the difference between the vertical and horizontal line tests?
  3. Can a one-to-one function have any repeated values for different inputs?
  4. How does the inverse of a one-to-one function behave?
  5. What types of functions (e.g., linear, quadratic, etc.) are typically not one-to-one?

Tip: Always remember, a function is one-to-one if no two different inputs have the same output!

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
Graphing

Formulas

-

Theorems

Horizontal Line Test

Suitable Grade Level

Grades 9-12