Which of these is true of the rational function f(x)=(1 point)

Question

The domain is all real numbers.

There is a hole at (0.1)

The graph passes through the origin.

All of these are true.

Answer 1

To evaluate the statement about the rational function \( f(x) \), we need to consider each option:

1. The domain is all real numbers: This is not true for a rational function unless it has no restrictions in its expression. For rational functions, the domain excludes any values of \( x \) that make the denominator equal to zero.

2. There is a hole at (0.1): Without the specific function defined (since "f(x)=(" seems incomplete), we cannot determine if there is indeed a hole at that point. A hole occurs when a factor in the numerator and denominator cancels out, suggesting that a certain point is not included in the function.

3. The graph passes through the origin: For the graph to pass through the origin, \( f(0) \) would need to be defined and equal to 0. Again, without more information about the function, we cannot confirm if this is true.

4. All of these are true: Since the first point about the domain is false, this cannot be true.

Since we don't have enough information from the incomplete function stated and there are uncertainties in all statements, none of the individual statements can be confirmed as true without additional information. Therefore, the correct answer would be to not assert that any of these statements are definitively true as they stand.