The graph below shows the polynomial: $$f(x) = (x-1)^k$$ Use the slider to change the exponent $k\text{,}$ and observe the changes to the graph. There are a few things to take note of here:

1. The graph’s only root is at: ? x y $=$
2. When the exponent is odd, the graph ? crosses over bounces off the $x$-axis at the $x$-intercept.
3. When the exponent is even, the graph ? crosses over bounces off the $x$-axis at the $x$-intercept.
4. Near the $x$-intercept, the graph becomes ? more horizontal more vertical as the exponent increases.