Question

How to Determine If a Function Is One to One

A: Vertical Line Test |
B: Horizontal Line Test |
C: Inverse Function Test |
D: Concavity Test

Answer 1

To determine if a function is one-to-one, we can use different tests such as the vertical line test, horizontal line test, inverse function test, and concavity test.

Step-by-step explanation:

To determine if a function is one-to-one, we can use the inverse function test. If a function is one-to-one, it means that no two different inputs will produce the same output. To test this, we can find the inverse function of the given function. If the inverse function exists and is also a function, then the original function is one-to-one.

1. Vertical Line Test: This test is used to determine if a graph represents a function. If every vertical line intersects the graph at most once, then the function is one-to-one.
2. Horizontal Line Test: This test is used to determine if a graph represents a one-to-one function. If every horizontal line intersects the graph at most once, then the function is one-to-one.
3. Inverse Function Test: This test involves finding the inverse function of the given function. If the inverse function exists and is also a function, then the original function is one-to-one.
4. Concavity Test: This test is used to determine if a function is one-to-one. If the function is concave up or down (i.e., the graph is always increasing or always decreasing), then the function is one-to-one.