Look at the graph attached complete each sentence  the vertical function is  the horizontal function is  options: x=3, x=-3, x=1, x=-1, y=3, y=-3, y=1, y=-1

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Look at the graph attached complete each sentence 

the vertical function is 

the horizontal function is 

options: x=3, x=-3, x=1, x=-1, y=3, y=-3, y=1, y=-1

### Rational Function Graph Analysis

Look at the graph.

#### Graph Explanation:

This graph represents the function \( f(x) = \frac{x - 1}{x + 3} \).

- **Axes and Scale:** 
  - The horizontal axis (x-axis) and the vertical axis (y-axis or \( f(x) \)-axis) are clearly marked from -6 to 6. 
  - Each unit on the grid represents an increment of 1.

- **Function Behavior:**
  - The function has a vertical asymptote at \( x = -3 \). This is where the function is undefined because the denominator becomes zero.
  - The function has a horizontal asymptote at \( y = 1 \). This can be observed as the graph approaches \( y = 1 \) as \( x \) increases or decreases towards infinity. 
  - There is no intersection of the graph with the vertical asymptote.
  - The graph intersects the y-axis at \( y = \frac{-1}{3} \) and it crosses the x-axis at the point \( (1, 0) \).

- **Curve Description:**
  - For \( x < -3 \), the graph approaches negative infinity as it gets closer to \( x = -3 \), and it continues to decrease very steeply as \( x \) moves further left.
  - For \( x > -3 \), the graph increases and moves towards positive infinity as it gets closer to \( x = -3 \), then it crosses the x-axis at \( (1, 0) \) and continues to approach the horizontal asymptote \( y = 1 \).

This graph visually illustrates the properties and behavior of the rational function \( \frac{x - 1}{x + 3} \), highlighting key features such as asymptotes and intercepts.
Transcribed Image Text:### Rational Function Graph Analysis Look at the graph. #### Graph Explanation: This graph represents the function \( f(x) = \frac{x - 1}{x + 3} \). - **Axes and Scale:** - The horizontal axis (x-axis) and the vertical axis (y-axis or \( f(x) \)-axis) are clearly marked from -6 to 6. - Each unit on the grid represents an increment of 1. - **Function Behavior:** - The function has a vertical asymptote at \( x = -3 \). This is where the function is undefined because the denominator becomes zero. - The function has a horizontal asymptote at \( y = 1 \). This can be observed as the graph approaches \( y = 1 \) as \( x \) increases or decreases towards infinity. - There is no intersection of the graph with the vertical asymptote. - The graph intersects the y-axis at \( y = \frac{-1}{3} \) and it crosses the x-axis at the point \( (1, 0) \). - **Curve Description:** - For \( x < -3 \), the graph approaches negative infinity as it gets closer to \( x = -3 \), and it continues to decrease very steeply as \( x \) moves further left. - For \( x > -3 \), the graph increases and moves towards positive infinity as it gets closer to \( x = -3 \), then it crosses the x-axis at \( (1, 0) \) and continues to approach the horizontal asymptote \( y = 1 \). This graph visually illustrates the properties and behavior of the rational function \( \frac{x - 1}{x + 3} \), highlighting key features such as asymptotes and intercepts.
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