To determine the range of the function $ h $, we need to understand the possible values that $ h(x) $ can take. Here are the steps to find the range:

1. **Identify the function $ h(x) $**: The problem does not provide the explicit form of $ h(x) $, so we will assume it is a general function. If you have the specific form of $ h(x) $, please provide it.

2. **Analyze the function**: If $ h(x) $ is a common function like a polynomial, rational function, trigonometric function, etc., we can analyze its behavior to determine the range.

3. **Consider the domain**: The range of a function depends on its domain. Ensure you know the domain of $ h(x) $.

4. **Evaluate the function**: Determine the minimum and maximum values (if they exist) that $ h(x) $ can take. This can involve finding critical points, asymptotes, or limits.

Since the problem mentions labels like $ \infty $, $ y $, $ -4 $, $ -2 $, $ x $, $ 2 $, $ -1 $, and $ -\infty $, we can infer that these might be potential values or boundaries for the range.

### Example Analysis (Assuming a Quadratic Function)
Let's assume $ h(x) = x^2 - 4 $ as an example:

1. **Identify the function**: $ h(x) = x^2 - 4 $.

2. **Analyze the function**: This is a quadratic function that opens upwards (since the coefficient of $ x^2 $ is positive).

3. **Consider the domain**: The domain of $ h(x) $ is all real numbers ($ -\infty

Question

To determine the range of the function $ h $, we need to understand the possible values that $ h(x) $ can take. Here are the steps to find the range:

1. **Identify the function $ h(x) $**: The problem does not provide the explicit form of $ h(x) $, so we will assume it is a general function. If you have the specific form of $ h(x) $, please provide it.

2. **Analyze the function**: If $ h(x) $ is a common function like a polynomial, rational function, trigonometric function, etc., we can analyze its behavior to determine the range.

3. **Consider the domain**: The range of a function depends on its domain. Ensure you know the domain of $ h(x) $.

4. **Evaluate the function**: Determine the minimum and maximum values (if they exist) that $ h(x) $ can take. This can involve finding critical points, asymptotes, or limits.

Since the problem mentions labels like $ \infty $, $ y $, $ -4 $, $ -2 $, $ x $, $ 2 $, $ -1 $, and $ -\infty $, we can infer that these might be potential values or boundaries for the range.

### Example Analysis (Assuming a Quadratic Function)
Let's assume $ h(x) = x^2 - 4 $ as an example:

1. **Identify the function**: $ h(x) = x^2 - 4 $.

2. **Analyze the function**: This is a quadratic function that opens upwards (since the coefficient of $ x^2 $ is positive).

3. **Consider the domain**: The domain of $ h(x) $ is all real numbers ($ -\infty < x < \infty $).

4. **Evaluate the function**:
   - The vertex of the parabola $ y = x^2 - 4 $ is at $ (0, -4) $.
   - As $ x $ approaches $ \infty $ or $ -\infty $, $ h(x) $ approaches $ \infty $.

Therefore, the minimum value of $ h(x) $ is $ -4 $, and there is no maximum value (it goes to $ \infty $).

### Range
The range of $ h(x) = x^2 - 4 $ is $ [-4, \infty) $.

### Label Placement
Based on the example function $ h(x) = x^2 - 4 $:
- The minimum value is $ -4 $.
- The function increases without bound, so the range extends to $ \infty $.

Thus, the correct labels for the range of $ h $ would be $ -4 $ and $ \infty $.

If you provide the specific form of $ h(x) $, I can give a more precise answer.

Knowee AI · Accepted Answer