One To One Function 450B03

1. **State the problem:** We need to determine which of the given equations represents a one-to-one function. 2. **Recall the definition:** A function is one-to-one if each output corresponds to exactly one input. Graphically, this means the function passes the Horizontal Line Test. 3. **Analyze each equation:** - Equation 1: $$y = -2x + 6$$ is a linear function with slope $$-2$$. Linear functions with non-zero slope are one-to-one because they pass the Horizontal Line Test. - Equation 2: $$x = 3$$ is a vertical line. This is not a function of $$x$$ (does not pass the Vertical Line Test), so it cannot be one-to-one. - Equation 3: $$y = x^2 - 4x + 5$$ is a quadratic function. Quadratic functions are generally not one-to-one because they fail the Horizontal Line Test (they are parabolas). - Equation 4: $$y = 4$$ is a horizontal line. This is a constant function, which is not one-to-one because multiple inputs map to the same output. 4. **Conclusion:** The only one-to-one function among the options is $$y = -2x + 6$$. **Final answer:** $$y = -2x + 6$$