Question

Can you draw different functions that have the same x-intercepts and the same domain and range?

Answer 1

I'm pretty sure the answer is no.  A function looks like this: f(x) = mx + c.  Let's add another function, f(y) = ny + d.  If the x-intercept is the same, we can subtract c and d from their respective equations. f(x) = mx, f(y) = ny. If the domains are the same, then x and y can have the same value, so we divide it out. f(x) = m, f(y) = n.  Finally, if the ranges are the same, the value of f(x) = f(y).  So by the substitution property, m=n.  Since all the variables equal each other, both functions are equal to f(x) = mx+c!  Therefore, they can only be the same function.

Answer: No