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.).