To determine the range of the function shown in the image, let’s examine the graph, which appears to be a parabola opening upwards. The vertex of this parabola is at the lowest point, located at $y = -4$.

Analyzing the Range

For a parabola that opens upwards, the range is determined from the minimum $y$-value (the vertex) and extends to positive infinity.

• The minimum $y$-value is $-4$, and the values go upwards from there.
• Therefore, the range of this function is $y \geq -4$.

Answer

The correct option for the range of the function is:

• $y \geq -4$

Would you like more details on analyzing the range of quadratic functions or other questions related to this topic?

Here are some related questions to deepen your understanding:

1. How do we determine the vertex of a quadratic function graphically and algebraically?
2. What does it mean for a parabola to open upwards or downwards, and how does this affect the range?
3. How can we find the range of functions that are not quadratic?
4. How do we identify domain and range differences between linear and quadratic functions?
5. Can a quadratic function have a maximum point instead of a minimum?

Tip: For parabolas, remember that the range is always dependent on whether the parabola opens upwards or downwards.