Depic a function for the graphjust in case you can’t see the numbers are -3, (0,0), 3 ### Understanding Asymptotes and Graphing Rational Functions#### Explanation of the GraphThe graph depicted is of a rational function, illustrating its behavior around vertical and horizontal asymptotes.#### Key Features of the Graph:1. **Axes and Scale:** - The x-axis (horizontal axis) and y-axis (vertical axis) are clearly marked. - Significant points are labeled along the axes: on the x-axis at -3, 0, and 3; and on the y-axis at 1.2. **Vertical Asymptotes:** - The graph has vertical dashed lines at $ x = -1 $ and $ x = 1 $. These lines represent the vertical asymptotes of the function. - As $ x $ approaches -1 and 1 from both the left and right, the function's value increases or decreases without bound, indicating it approaches infinity or negative infinity.3. **Function Behavior and Horizontal Asymptote:** - For large values of $ |x| $ (both positive and negative), the function approaches a value near the x-axis, indicating that the x-axis ($ y = 0 $) is a horizontal asymptote. - The function appears to have significant changes in its direction as it approaches the vertical asymptotes, particularly near $ x = -1 $ and $ x = 1 $.#### Interpretation:1. **Behavior Near Vertical Asymptotes:** - As the function approaches $ x = -1$ from the left, it decreases towards negative infinity. - As it passes $ x = -1$ from the right, it increases towards positive infinity. - Similarly, as it approaches $ x = 1$ from the left, it increases towards positive infinity, and from the right, it decreases towards negative infinity.2. **Horizontal Asymptote:** - The graph indicates that as $ x $ moves away from the origin (both positive and negative directions), the function value approaches zero. This means the function has a horizontal asymptote at $ y = 0 $.Understanding the characteristics and behaviors illustrated by this graph is crucial for comprehending the nature of rational functions and their asymptotes. This foundational concept is fundamental in further exploring more complex mathematical functions and their graphical representations.

Answered: Depic a function for the graph just in…

Math

Algebra

Depic a function for the graph just in case you can’t see the numbers are -3, (0,0), 3

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: 200 (0, 180) 150 (4, 133.2) (8, 98.57) 100 (12, 72.94) (16, 53.98) 50 0- 2 4 8 10 12 14 16 18 20…

A: The given graph is

Q: The graph of f is given. 4 -1

A: We can use the concept of inverse function in order to solve the given problem.

Q: You are given the graphs of certain functions. Determine if the function is even, odd, or neither.…

A: EVEN FUNCTION : A function is said to be even if the graph of that function show symmetry about…

Q: 3- 1 1 2 -5

Q: Choose the range that best describes the piecewise defined function in the graph below -8 -6 -4 -2…

Q: Find the domain of the function graphed. 2. 24600 8. www ********* www **** www. X

Q: 3 2 1] 2 -1 -1 -2 -3 -4 4)

A: Graphically, we know that roots of a function are those points on x-axis where graph of the function…

Q: Is the graph a function? (-)

Q: Do the data in the following table represent a function? Explain your answer. nput (x) 4 8 11 Dutput…

Q: 2. (2X x <2

Q: e function by the graph

A: Here we have to find the parent function ,

Q: Use the graph of the function f shown to the right to answer parts (a)-(n). 4 (-3,3) (a) Find f( -…

A: Refer to the question we need to calculate the value at the provided point with the use of provided…

Q: Complete a function analysis of the graph below: 10- 5- -10 -5 Domain Select ]

Q: Your answer is incorrect. Graph the function. y--33 Plot five points on the graph of the function:…

Q: 7. 6.

A: Vertical line test: The vertical line test can be used to determine whether a graph represents a…

Q: Write the formula to define the piecewise function shown in the graph. (48, 49) y 50 40 30- (-5, 30)…

A: A piecewise function is used to define a function that behaves differently at different intervals of…

Q: The graph of y=f(x) is given. Graph the function y=2f(x-3)+5.

A: The graph of y=fx is given below. To determine the graph of the function y=2fx−3+5.

Q: 6 fy 2 -6 -4 -2 2 4 6. -2 -4 -6 4.

Q: How would I find the domain and range of this function

A: NOTE: Refresh your page if you can't see any equations. .

Question

Depic a function for the graph

just in case you can’t see the numbers are

-3, (0,0), 3

### Understanding Asymptotes and Graphing Rational Functions

#### Explanation of the Graph

The graph depicted is of a rational function, illustrating its behavior around vertical and horizontal asymptotes.

#### Key Features of the Graph:

1. **Axes and Scale:**
- The x-axis (horizontal axis) and y-axis (vertical axis) are clearly marked.
- Significant points are labeled along the axes: on the x-axis at -3, 0, and 3; and on the y-axis at 1.

2. **Vertical Asymptotes:**
- The graph has vertical dashed lines at $ x = -1 $ and $ x = 1 $. These lines represent the vertical asymptotes of the function.
- As $ x $ approaches -1 and 1 from both the left and right, the function's value increases or decreases without bound, indicating it approaches infinity or negative infinity.

3. **Function Behavior and Horizontal Asymptote:**
- For large values of $ |x| $ (both positive and negative), the function approaches a value near the x-axis, indicating that the x-axis ($ y = 0 $) is a horizontal asymptote.
- The function appears to have significant changes in its direction as it approaches the vertical asymptotes, particularly near $ x = -1 $ and $ x = 1 $.

#### Interpretation:

1. **Behavior Near Vertical Asymptotes:**
- As the function approaches $ x = -1$ from the left, it decreases towards negative infinity.
- As it passes $ x = -1$ from the right, it increases towards positive infinity.
- Similarly, as it approaches $ x = 1$ from the left, it increases towards positive infinity, and from the right, it decreases towards negative infinity.

2. **Horizontal Asymptote:**
- The graph indicates that as $ x $ moves away from the origin (both positive and negative directions), the function value approaches zero. This means the function has a horizontal asymptote at $ y = 0 $.

Understanding the characteristics and behaviors illustrated by this graph is crucial for comprehending the nature of rational functions and their asymptotes. This foundational concept is fundamental in further exploring more complex mathematical functions and their graphical representations.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Power Series$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

can you please write it with a good handwritting please im begging thank you i cannot read it please write it with normal type like how normal lines in books are thank you
Sigh.. I tried can someone help me understand this.
5- -5 5 -5- Determine the values of a, b, c, and d so the function (a - a) (x + 1) (x + b) (x- c) (x + d) (x + 3) f (x) = correctly model the graph. (a, b, c, and d are all whole numbers) a = 5,
Please circle the answer and specify so I can understand. There are several sections in this question and specify the answer of each section related to that question so that I know. I appreciate your understanding.
Help