https://file.aiquickdraw.com/mathbot/file/1728584697270kkffu5ms.jpg

Let's analyze the functions one by one to identify the correct graph descriptions:

1. **\( k(x) = x + 1 \)**:
   - This is a linear function of the form \( y = mx + b \), where the slope \( m = 1 \) and the y-intercept is \( 1 \).
   - Since the slope is positive, this function represents a **line with a positive slope**.

2. **\( g(x) = x^2 - 4 \)**:
   - This is a quadratic function of the form \( y = ax^2 + bx + c \), where \( a = 1 \) (positive).
   - Quadratic functions with a positive leading coefficient \( a \) have parabolas that open **upward**. Thus, this represents a **parabola opening up**.

3. **\( h(x) = 0 \)**:
   - This function is a constant function, where the output is always 0, which means it represents a **horizontal line**.

Now let's fill in the table based on this analysis:

- For \( k(x) = x + 1 \), select **line with a positive slope**.
- For \( g(x) = x^2 - 4 \), select **parabola opening up**.
- For \( h(x) = 0 \), select **horizontal line**.

Would you like further details or explanations on any of these functions?

### Related Questions:
1. What is the general form of a linear function, and how does the slope affect its graph?
2. How can you identify the direction in which a parabola opens based on its equation?
3. What are the characteristics of constant functions, and how do they graph?
4. How do the values of \( a \), \( b \), and \( c \) in a quadratic equation affect the shape and position of its graph?
5. Can a linear function have a horizontal or vertical slope, and how does that affect its graph?

### Tip:
When analyzing the graph of a function, always check the highest power of \( x \) (degree) to determine its basic shape (linear, quadratic, etc.).

For each function, choose the correct description of its graph.

This problem involves identifying the graph of different types of functions: linear, quadratic, and constant. Learn how to determine whether the graph is a line or a parabola, and whether the slope is positive, negative, or zero.

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