Determine whether the following statement is true or false. If false, then give a counter example. The function f(x) = mx+b is a one-to-one function for all values of m and b.

Question

anonymous · Answer

On my test, I put false and I got it wrong. But I don't know why.....

kmeis002 · Answer

A one to one function is defined as every y value has a unique x value associated with it. Graphically, you may be use to the function test called the vertical line test. However, for a 1 to 1 function, it can pass the "horizontal line" test. Graphically, if a horizontal line intersects a function twice, this means that the function has two x values that return the same y. 
Y = mx+ b is a linear function and it will pass the horizontal line test, therefore it is 1 to 1. If you put false, you would also have to find a case which proves it is false, and this is impossible to do.

kmeis002 · Answer

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anonymous · Answer

One of my friends, who also got it wrong, said what if we said m=0 and b$$neq0$$. That would create a horizontal line, making all of the x-values = that number.  Would the produce an appropriate counterexample as well?

anonymous · Answer

b doesnt = 0

kmeis002 · Answer

Correct, that I misread, that is true. If m = 0 it will not be 1 to 1, but to get full credit you would have to list that example. If you friend said that, it should have been fine, but b can be any number for this example.

anonymous · Answer

Ok, Great! I appreciate your help.  I had a friend wake me up this morning and tell me that our test corrections were due!  That was a shocker!!!! Thanks, I didn't do too well on this test and you helped me understand it.  Once again, thanks for your help.

kmeis002 · Answer

He may have gotten it wrong by listing b cant be zero, because it can be zero and no longer be 1 to 1. I guess thats up to the discretion of your teacher.