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Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?The graph of f(x) passes the vertical line test.f(x) is a one-to-one function.The graph of the inverse of f(x) passes the horizontal line test.f(x) is not a function.

User Marek Maszay
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Answer: Choice B) f(x) is a one-to-one function

What this means is that each x input lands on a unique y output. For example, plugging x = 0 leads to y = -3. No other x value will lead to y = -3. This allows us to find the inverse.

The vertical line test is used to see if we have a function or not. The horizontal line test is used to see if an inverse is possible.

The phrasing "The graph of the inverse of f(x) passes the horizontal line test" is close, but we need to erase "the inverse of" to have choice C be useful. In other words, if choice C said "The graph of f(x) passes the horizontal line test", then it would be correct and useful.

Side note: Another term for "one-to-one" is "injective".

User Andrii Muzalevskyi
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