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Sagot :
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.
### 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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