Questions on 1-1 Functions
In this worksheet, you will be tasked with finding various functions that have certain properties. You can use the applet below to enter your function and check if it has the properties required. There are many valid solutions to each question, so an answer is not provided. Instead a hint is given, to aid you come up with your own answer.
Is the function graphed above, that is a 1-1 function? Explain.
Find a function that is 1-1.
Find a 1-1 function that is not increasing.
Find a 1-1 function that is not increasing and has .
Find a 1-1 function that is not a polynomial.
Give an example of a function that is not 1-1.
Give a counterexample to the claim that all 1-1 functions are increasing.
Give a counterexample to the claim that all 1-1 functions are onto.
Is it always true that all 1-1 functions are polynomials? Give an example to support your answer.
Is it always true that all polynomials are 1-1 functions? Give an example to support your answer.