True or False on One-to-One Function

[gracemccaghey03]

True or False. If false, change the statement to make it true (do not use cannot equal or the word "not").

Statement: g(x)=(x+1)^2 is a one-to-one function because it passes the vertical line test.

 

[Harry_the_cat]

So we can help you, here are some questions so we know what you know:
1. What defines a "function"?
2. What is meant by "one-to-one"?
3. What is the "vertical line" test and what does it determine?

 

[pka]

True or False. If false, change the statement to make it true (do not use cannot equal or the word "not"). Statement: g(x)=(x+1)^2 is a one-to-one function because it passes the vertical line test.

The vertical line test is for testing a graph for being that of a function: in a function no two pairs may have the same first term.
The horizontal line test is for testing a graph for being that of a one-to-one function: in a one-to-one function no two pairs may have the same second term.

 

[nanase]

i thought horizontal line test is to check if it is many-to-one function?

 

[pka]

i thought horizontal line test is to check if it is many-to-one function?

Consider the function \(\displaystyle f(x)=x^5+3\) See here. Any horizontal line, \(\displaystyle y=h\), intersects the graph of \(\displaystyle f\) at one point \(\displaystyle (\sqrt[5]{h-3},h)\)
If any horizontal line intersects the graph more than once then the function is not one-to-one. In that case your understanding is correct.

 

[Dr.Peterson]

i thought horizontal line test is to check if it is many-to-one function?

Assuming that you define "many-to-one" as "not one-to-one", then you could express it equally well either way. In my experience we usually focus on the special case, one-to-one, as what we are testing for, just as we say that the vertical line test is a test for a function, not for a one-to-many relation.