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```markdown
| Function f | Function g | Function h |
|-------------|--------------------|----------------------|
| Domain: [tex]$(-\infty, \infty)$[/tex] | [tex]$y$[/tex]-intercept: [tex]$(0,3)$[/tex] | [tex]$y$[/tex]-intercept: [tex]$(0,-3)$[/tex] |
| [tex]$x$[/tex]-intercept: [tex]$(1,0)$[/tex] | [tex]$x \rightarrow 0$[/tex]: [tex]$(-3,0)$[/tex] | [tex]$r = \operatorname{ln}g \alpha (-\infty, 3]$[/tex] |
| Vertex: [tex]$(2,-3)$[/tex] | Maximum value: 4 | Axis of symmetry: [tex]$x=2$[/tex] |

Compare the characteristics of each function as listed above.
```

Sagot :

GinnyAnswer
Let's go through the question by given functions and provided descriptions.

### Function: Functimenf
- Domain: The domain of Functimenf is all real numbers. It is stated that the domain is [tex]\((-\infty, \infty)\)[/tex]. So this means that Functimenf can take any real number as an input.

Therefore, the domain is:
[tex]\[ (-\infty, \infty) \][/tex]

### Function: Furciong
- Y-intercept: The y-intercept of Furciong is given as (0, 3). This means that when [tex]\( x = 0 \)[/tex], the value of Furciong is 3. So,
[tex]\[ \text{Y-intercept: } (0, 3) \][/tex]

- X-intercept: The x-intercept is (1, 0), meaning when [tex]\( y = 0 \)[/tex], the value of [tex]\( x \)[/tex] is 1. So,
[tex]\[ \text{X-intercept: } (1, 0) \][/tex]

- Behavior as [tex]\( x \)[/tex] approaches -3: It's given that as [tex]\( x \)[/tex] approaches -3 from either the left or the right, the [tex]\( y \)[/tex] value approaches 0. Therefore,
[tex]\[ \text{Behavior: As \( x \) approaches -3, \( y \) value approaches 0} \][/tex]

### Function: Furctionh
- Y-intercept: The y-intercept of Furctionh is given as (0, -3). This means when [tex]\( x = 0 \)[/tex], the value of Furctionh is -3. So,
[tex]\[ \text{Y-intercept: } (0, -3) \][/tex]

- Range: The range of Furctionh is given as [tex]\((-\infty, 3]\)[/tex]. This means Furctionh can take any value from negative infinity to 3 inclusive. So,
[tex]\[ \text{Range: } (-\infty, 3] \][/tex]

- Maximum Value: Furctionh has a maximum value of -3 at the vertex point (2, -3). This means that the highest value Furctionh can reach is -3 when [tex]\( x = 2 \)[/tex]. So,
[tex]\[ \text{Maximum value at vertex: } (2, -3) \][/tex]

- Discontinuity: There is a discontinuity at [tex]\( x = 2 \)[/tex]. This means that Furctionh is not defined or has a break at [tex]\( x = 2 \)[/tex]. So,
[tex]\[ \text{Discontinuity at: \( x = 2 \)} \][/tex]

In summary, here is the detailed information for each function:

### Summary
- Functimenf
- Domain: [tex]\((-\infty, \infty)\)[/tex]

- Furciong
- Y-intercept: (0, 3)
- X-intercept: (1, 0)
- Behavior: As [tex]\( x \)[/tex] approaches -3, [tex]\( y \)[/tex] value approaches 0

- Furctionh
- Y-intercept: (0, -3)
- Range: [tex]\((-\infty, 3]\)[/tex]
- Maximum value at vertex: (2, -3)
- Discontinuity at: [tex]\( x = 2 \)[/tex]

This is the complete step-by-step analysis based on the given table and inferred descriptions for each function.
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