SOLUTION: Is the given function {{{f(x)=x^2-4}}} one-to-one? Why or why not?

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Question 128490: Is the given function f%28x%29=x%5E2-4 one-to-one? Why or why not?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Notice if we graph f%28x%29=x%5E2-4, we get


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-4%29+



From the graph, we can see that the curve violates the horizontal line test. In other words, if you pass a straightedge horizontally through the graph, the straightedge will touch two points. So the function is not one-to-one.