### Home > INT3 > Chapter 1 > Lesson 1.1.2 > Problem1-15

1-15.

Rhianna says she can draw different functions that have the same $x$-intercepts and the same domain and range. Her teammates say, “No, that’s impossible!” But Rhianna insists, “It is possible, we just need to sketch the graphs.”

1. What if the $x$-intercepts are $(-5,0)$, $(2,0)$, and $(6,0)$, the domain is $-5\le x\le7$, and the range is $-4\le y\le10$? Is there more than one possible function? Give examples to help explain why or why not.

2. What if the $x$-intercepts are $(-4,0)$ and $(2,0)$, the domain is all real numbers, and the range is $y\ge-8$? Is there more than one possible function? Give examples of multiple functions or explain why there can be only one.

You can create a graph with multiple turns and dips.