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

Answer 1

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

1. The solutions are complex numbers - This is always true if the function has no real roots. Complex roots exist when a polynomial does not intersect the x-axis.

2. The graph does not touch the x-axis - This is also true for a function with no real roots. If it has no real roots, it does not cross or touch the x-axis.

The other statements about solutions being irrational and the graph not touching the y-axis are not always true. The graph can still touch the y-axis for functions with no real roots, and the roots can be complex (which may not necessarily be irrational).

Therefore, the statements that are always true are:

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