Parabola Function Analysis: Finding Positive Values Above X-Axis

Question

The graph of the function below does not intersect the x x -axis.

The parabola's vertex is marked A.

Find all values of x x where
f\left(x\right) > 0 .

AAAX

Step-by-Step Solution

Based on the given graph characteristics, we conclude that the parabola never intersects the x x -axis and is therefore entirely above it due to opening upwards. This means the function is always positive for every x x .

Thus, the correct choice is:

  • Choice 3: The domain is always positive.

Therefore, the solution to the problem is the domain is always positive.

Answer

The domain is always positive.