Question

Select all that are always true of a function that has no real roots: (2 points)
Responses

the solutions are irrational numbers
the solutions are irrational numbers

the graph does not touch the x-axis
the graph does not touch the x-axis

the graph does not touch the y-axis
the graph does not touch the y-axis

the solutions are complex numbers

Answer 1

For a function that has no real roots, the following statements are always true:

1. **The graph does not touch the x-axis.**
2. **The solutions are complex numbers.**

The other statements about the solutions being irrational numbers or the graph not touching the y-axis are not necessarily true.

In summary, the correct selections are:

- the graph does not touch the x-axis
- the solutions are complex numbers