Do you think it's possible to create a function with any given set of x- intercepts?

An x-intercept is where y is zero. With the law of mutiplying by zero, we know that: If a * b = 0, then a, b, or both must be zero. So if we want that a function will be zero at 4 and 2, we need to find a function which equals zero at these points. x = 2 / subtract 2 from both sides. x - 2 = 0 So the expression is (x - 2). The expression for x = 4 is (x - 4). Now we just multiply them and give the function a name: y = (x - 2)(x - 4) y = x^2 - 6x + 8. 2. Same idea: y = (x + 6)(x - 3) y = x^2 +3x - 18. 3. Once again, same idea: y = (x + 5)(x - 5)(x - 1) Since (x + 5)(x - 5) = x^2 - 25, we can calculate: y = (x^2 -25)(x - 1) y = x^3 - x^2 -25x + 25. 4. As explained above, yes. 5. Yes, there is an infinite number of functions that fit the conditions of those questions. Just multiply the same factor over and over: For 1: y = (x - 2)(x - 2)(x - 4) y = (x^2 - 6x + 8)(x - 2) y = x^3 - 8x^2 + 20x - 16. The same goes for 2 and 3.