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What are the features of the function [tex]g(x) = f(x+4) + 8[/tex]?

- Domain: [tex]$(4, \infty)$[/tex]
- [tex]$x$[/tex]-intercept at [tex]$(1,0)$[/tex]
- Vertical asymptote at [tex]$x=-4$[/tex]
- [tex]$y$[/tex]-intercept at [tex]$(0,10)$[/tex]
- Range: [tex]$(8, \infty)$[/tex]

Sagot :

GinnyAnsweridn
Sure! Let's carefully analyze the given features of the function [tex]\( g(x) \)[/tex] given by the transformation [tex]\( g(x) = f(x + 4) + 8 \)[/tex].

### 1. Domain:
The domain of [tex]\( g(x) \)[/tex] is given as [tex]\( (4, \infty) \)[/tex].

### 2. [tex]\( x \)[/tex]-Intercept:
The [tex]\( x \)[/tex]-intercept of [tex]\( g(x) \)[/tex] is given as [tex]\( (1,0) \)[/tex].

### 3. Vertical Asymptote:
The vertical asymptote of [tex]\( g(x) \)[/tex] is given as [tex]\( x = -4 \)[/tex].

### 4. [tex]\( y \)[/tex]-Intercept:
The [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex] is given as [tex]\( (0,10) \)[/tex].

### 5. Range:
The range of [tex]\( g(x) \)[/tex] is given as [tex]\( (8, \infty) \)[/tex].

Given all this information, we can summarize the features of the function [tex]\( g \)[/tex] as follows:

1. Domain: [tex]\( (4, \infty) \)[/tex]
2. [tex]\( x \)[/tex]-Intercept: [tex]\( (1, 0) \)[/tex]
3. Vertical Asymptote: [tex]\( x = -4 \)[/tex]
4. [tex]\( y \)[/tex]-Intercept: [tex]\( (0, 10) \)[/tex]
5. Range: [tex]\( (8, \infty) \)[/tex]

These features describe the behavior of the transformed function [tex]\( g(x) \)[/tex].
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